Mix Examples-Thermodynamics Questions in English

Column $I$ contains a list of processes involving the expansion of an ideal gas. Match this with Column $II$ describing the thermodynamic change during this process.

Column $I$	Column $II$
$(A)$ An insulated container has two chambers separated by a valve. Chamber $I$ contains an ideal gas and Chamber $II$ has a vacuum. The valve is opened.	$(p)$ The temperature of the gas decreases
$(B)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $P \propto V^{-2}$	$(q)$ The temperature of the gas increases or remains constant
$(C)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $P \propto V^{-4/3}$	$(r)$ The gas loses heat
$(D)$ An ideal monoatomic gas expands such that its pressure $P$ and volume $V$ follow the behavior shown in the graph	$(s)$ The gas gains heat

$A$ gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i = 10^5 \text{ Pa}$ and volume $V_i = 10^{-3} \text{ m}^3$ changes to a final state at $P_f = (1/32) \times 10^5 \text{ Pa}$ and $V_f = 8 \times 10^{-3} \text{ m}^3$ in an adiabatic quasi-static process, such that $P^3 V^5 = \text{constant}$. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at $P_i$, followed by an isochoric (isovolumetric) process at volume $V_f$. The amount of heat supplied to the system in the two-step process is approximately: (in $\text{ J}$)

One mole of an ideal gas expands adiabatically from an initial state $(T_A, V_0)$ to a final state $(T_f, 5 V_0)$. Another mole of the same gas expands isothermally from a different initial state $(T_B, V_0)$ to the same final state $(T_f, 5 V_0)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_A / T_B$?

One mole of an ideal gas undergoes two different cyclic processes $I$ and $II$,as shown in the $P-V$ diagrams below. In cycle $I$,processes $a, b, c$ and $d$ are isobaric,isothermal,isobaric and isochoric,respectively. In cycle $II$,processes $a^{\prime}, b^{\prime}, c^{\prime}$ and $d^{\prime}$ are isothermal,isochoric,isobaric and isochoric,respectively. The total work done during cycle $I$ is $W_I$ and that during cycle $II$ is $W_{II}$. The ratio $W_I / W_{II}$ is . . . .

An ideal gas undergoes a cyclic thermodynamic process in different ways as shown in the corresponding $P-V$ diagrams in column $3$ of the table. Consider only the path from state $1$ to $2$. $W$ denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here $\gamma$ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is $n$.

Column $I$	Column $II$	Column $III$
$(I)$ $W_{1-2} = \frac{1}{\gamma-1}(P_2V_2 - P_1V_1)$	$(i)$ Isothermal	$(P)$ [Graph $P$]
$(II)$ $W_{1-2} = -P(V_2 - V_1)$	(ii) Isochoric	$(Q)$ [Graph $Q$]
$(III)$ $W_{1-2} = 0$	(iii) Isobaric	$(R)$ [Graph $R$]
$(IV)$ $W_{1-2} = -nRT \ln(\frac{V_2}{V_1})$	(iv) Adiabatic	$(S)$ [Graph $S$]

$(1)$ Which of the following options is the only correct representation of a process in which $\Delta U = \Delta Q - P \Delta V$?
$[A] (II) (iii) (P)$ $[B] (II) (iii) (R)$ $[C] (II) (iv) (S)$ $[D] (III) (iii) (P)$
$(2)$ Which one of the following options is the correct combination?
$[A] (III) (ii) (S)$ $[B] (II) (iv) (R)$ $[C] (II) (iv) (P)$ $[D] (IV) (ii) (S)$
$(3)$ Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?
$[A] (III) (iv) (R)$ $[B] (I) (ii) (Q)$ $[C] (I) (iv) (Q)$ $[D] (I) (iv) (R)$

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?
$(A)$ Process $I$ is an isochoric process
$(B)$ In process $II$,gas absorbs heat
$(C)$ In process $IV$,gas releases heat
$(D)$ Processes $I$ and $III$ are $not$ isobaric

The figure shows the $P-V$ plot of an ideal gas taken through a cycle $ABCDA$. The part $ABC$ is a semi-circle and $CDA$ is half of an ellipse. Then,
$(A)$ the process during the path $A \rightarrow B$ is isothermal
$(B)$ heat flows out of the gas during the path $B \rightarrow C \rightarrow D$
$(C)$ work done during the path $A \rightarrow B \rightarrow C$ is zero
$(D)$ positive work is done by the gas in the cycle $ABCDA$

One mole of a monatomic ideal gas is taken through a cycle $ABCDA$ as shown in the $P-V$ diagram. Column $II$ gives the characteristics involved in the cycle. Match them with each of the processes given in Column $I$.

Column $I$	Column $II$
$(A)$ Process $A \rightarrow B$	$(p)$ Internal energy decreases.
$(B)$ Process $B \rightarrow C$	$(q)$ Internal energy increases.
$(C)$ Process $C \rightarrow D$	$(r)$ Heat is lost.
$(D)$ Process $D \rightarrow A$	$(s)$ Heat is gained.
	$(t)$ Work is done on the gas.

$A$ reversible cyclic process for an ideal gas is shown below. Here,$P, V$,and $T$ are pressure,volume,and temperature,respectively. The thermodynamic parameters $q, w, H$,and $U$ are heat,work,enthalpy,and internal energy,respectively.
The correct option$(s)$ is (are):
$(A)$ $q_{AC} = \Delta U_{BC}$ and $W_{AB} = P_2(V_2 - V_1)$
$(B)$ $W_{BC} = P_2(V_2 - V_1)$ and $q_{BC} = H_{AC}$
$(C)$ $\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{BC}$
$(D)$ $q_{BC} = \Delta H_{AC}$ and $\Delta H_{CA} > \Delta U_{CA}$

$A$ reversible cyclic process for an ideal gas is shown below. Here,$P, V$,and $T$ are pressure,volume,and temperature,respectively. The thermodynamic parameters $q, w, H$,and $U$ are heat,work,enthalpy,and internal energy,respectively.
The correct option$(s)$ is (are):
$(A)$ $q_{AC} = \Delta U_{AC}$ and $W_{AB} = 0$
$(B)$ $W_{BC} = P_2(V_1 - V_2)$ and $q_{BC} = \Delta H_{BC}$
$(C)$ $\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{AC}$
$(D)$ $q_{BC} = \Delta H_{BC}$ and $\Delta H_{CA} > \Delta U_{CA}$

One mole of a monoatomic ideal gas goes through a thermodynamic cycle,as shown in the volume versus temperature $(V-T)$ diagram. The correct statement$(s)$ is/are :
[$R$ is the gas constant]
$(1)$ Work done in this thermodynamic cycle $(1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 1)$ is $|W| = \frac{1}{2} RT_0$
$(2)$ The ratio of heat transfer during processes $1 \rightarrow 2$ and $2 \rightarrow 3$ is $\left|\frac{Q_{1 \rightarrow 2}}{Q_{2 \rightarrow 3}}\right| = \frac{5}{3}$
$(3)$ The above thermodynamic cycle exhibits only isochoric and adiabatic processes.
$(4)$ The ratio of heat transfer during processes $1 \rightarrow 2$ and $3 \rightarrow 4$ is $\left|\frac{Q_{1 \rightarrow 2}}{Q_{3 \rightarrow 4}}\right| = \frac{1}{2}$

$A$ small particle of mass $m$ moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in the figure. When the distance of the piston from the closed end is $L = L_0$, the particle speed is $v = v_0$. The piston is moved inward at a very low speed $V$ such that $V \ll \frac{dL}{L} v_0$, where $dL$ is the infinitely small displacement of the piston. Which of the following statement(s) is/are correct?
$(1)$ The rate at which the particle strikes the piston is $v / (2L)$
$(2)$ After each collision with the piston, the particle speed increases by $2V$
$(3)$ The particle's kinetic energy increases by a factor of $4$ when the piston is moved inward from $L_0$ to $L_0 / 2$
$(4)$ If the piston moves inward by $dL$, the particle speed increases by $v \frac{dL}{L}$

Answer the following by appropriately matching the lists based on the information given in the paragraph.
In a thermodynamics process on an ideal monatomic gas,the infinitesimal heat absorbed by the gas is given by $T \Delta X$,where $T$ is the temperature of the system and $\Delta X$ is the infinitesimal change in a thermodynamic quantity $X$ of the system. For a mole of monatomic ideal gas,$X = \frac{3}{2} R \ln \left(\frac{T}{T_A}\right) + R \ln \left(\frac{V}{V_A}\right)$. Here,$R$ is the gas constant,$V$ is the volume of the gas,$T_A$ and $V_A$ are constants.
The $List-I$ below gives some quantities involved in a process and $List-II$ gives some possible values of these quantities.

List-$I$	List-$II$
$(I)$ Work done by the system in process $1 \rightarrow 2 \rightarrow 3$	$(P)$ $\frac{1}{3} R T_0 \ln 2$
$(II)$ Change in internal energy in process $1 \rightarrow 2 \rightarrow 3$	$(Q)$ $\frac{1}{3} R T_0$
$(III)$ Heat absorbed by the system in process $1 \rightarrow 2 \rightarrow 3$	$(R)$ $R T_0$
$(IV)$ Heat absorbed by the system in process $1 \rightarrow 2$	$(S)$ $\frac{4}{3} R T_0$
	$(T)$ $\frac{1}{3} R T_0 (3 + \ln 2)$
	$(U)$ $\frac{5}{6} R T_0$

If the process carried out on one mole of monatomic ideal gas is as shown in the figure in the $PV$-diagram with $P_0 V_0 = \frac{1}{3} R T_0$,the correct match is:
$(1)$ $I \rightarrow Q, II \rightarrow R, III \rightarrow P, IV \rightarrow U$
$(2)$ $I \rightarrow S, II \rightarrow R, III \rightarrow Q, IV \rightarrow T$
$(3)$ $I \rightarrow Q, II \rightarrow R, III \rightarrow S, IV \rightarrow U$
$(4)$ $I \rightarrow Q, II \rightarrow S, III \rightarrow R, IV \rightarrow U$
If the process on one mole of monatomic ideal gas is as shown in the $TV$-diagram with $P_0 V_0 = \frac{1}{3} R T_0$,the correct match is:
$(1)$ $I \rightarrow S, II \rightarrow T, III \rightarrow Q, IV \rightarrow U$
$(2)$ $I \rightarrow P, II \rightarrow R, III \rightarrow T, IV \rightarrow S$
$(3)$ $I \rightarrow P, II \rightarrow R, III \rightarrow Q, IV \rightarrow T$
$(4)$ $I \rightarrow P, II \rightarrow R, III \rightarrow T, IV \rightarrow P$
Give the answer for question $(1)$ and $(2)$.

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4 V_1$. After this,the gas expands adiabatically and its volume becomes $32 V_1$. The work done by the gas during isothermal and adiabatic expansion processes are $W_{\text{iso}}$ and $W_{\text{adia}}$,respectively. If the ratio $\frac{W_{\text{iso}}}{W_{\text{adia}}} = f \ln 2$,then $f$ is:

One mole of a monatomic ideal gas is taken along two cyclic processes $E \rightarrow F \rightarrow G \rightarrow E$ and $E \rightarrow F \rightarrow H \rightarrow E$ as shown in the $PV$ diagram. The processes involved are purely isochoric,isobaric,isothermal,or adiabatic. Match the paths in List-$I$ with the magnitudes of the work done in List-$II$ and select the correct answer using the codes given below the lists.

List-$I$	List-$II$
$P. \quad G \rightarrow E$	$1. \quad 160 P_0 V_0 \ln 2$
$Q. \quad G \rightarrow H$	$2. \quad 36 P_0 V_0$
$R. \quad F \rightarrow H$	$3. \quad 24 P_0 V_0$
$S. \quad F \rightarrow G$	$4. \quad 31 P_0 V_0$

Codes: $P \quad Q \quad R \quad S$

$A$ thermodynamic system is taken from an initial state $i$ with internal energy $U_i = 100 \ J$ to the final state $f$ along two different paths $iaf$ and $ibf$,as schematically shown in the figure. The work done by the system along the paths $ia$,$af$,$ib$ and $bf$ are $W_{ia} = 50 \ J$,$W_{af} = 200 \ J$,$W_{ib} = 50 \ J$ and $W_{bf} = 100 \ J$ respectively. The heat supplied to the system along the paths $iaf$ and $ibf$ are $Q_{iaf}$ and $Q_{ibf}$ respectively. If the internal energy of the system in the state $b$ is $U_b = 200 \ J$ and $Q_{iaf} = 500 \ J$,the ratio $Q_{ibf} / Q_{iaf}$ is:

In the figure,a container is shown to have a movable (frictionless) piston on top. The container and the piston are made of perfectly insulating material,allowing no heat transfer between the outside and inside. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow heat transfer. The lower compartment is filled with $2$ moles of an ideal monatomic gas at $700 \ K$,and the upper compartment is filled with $2$ moles of an ideal diatomic gas at $400 \ K$. The heat capacities per mole are: for monatomic gas,$C_v = \frac{3}{2} R, C_p = \frac{5}{2} R$; for diatomic gas,$C_v = \frac{5}{2} R, C_p = \frac{7}{2} R$.
$1.$ Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved,the final temperature of the gases will be:
$(A) 550 \ K$ $(B) 525 \ K$ $(C) 513 \ K$ $(D) 490 \ K$
$2.$ Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then the total work done by the gases until they achieve equilibrium will be:
$(A) 250 \ R$ $(B) 200 \ R$ $(C) 100 \ R$ $(D) -100 \ R$
Give the answer for questions $1$ and $2$.

An ideal monoatomic gas is confined in a horizontal cylinder by a spring-loaded piston (as shown in the figure). Initially,the gas is at temperature $T_1$,pressure $P_1$,and volume $V_1$,and the spring is in its relaxed state. The gas is then heated very slowly to temperature $T_2$,pressure $P_2$,and volume $V_2$. During this process,the piston moves out by a distance $x$. Ignoring the friction between the piston and the cylinder,the correct statement$(s)$ is(are):
$(A)$ If $V_2=2V_1$ and $T_2=3T_1$,then the energy stored in the spring is $\frac{1}{4}P_1V_1$
$(B)$ If $V_2=2V_1$ and $T_2=3T_1$,then the change in internal energy is $3P_1V_1$
$(C)$ If $V_2=3V_1$ and $T_2=4T_1$,then the work done by the gas is $\frac{7}{3}P_1V_1$
$(D)$ If $V_2=3V_1$ and $T_2=4T_1$,then the heat supplied to the gas is $\frac{41}{6}P_1V_1$

$List-I$ describes thermodynamic processes in four different systems. $List-II$ gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

$List-I$	$List-II$
$(I)$ $10^{-3} \, kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 \, Pa$. The volume of the system changes from $10^{-6} \, m^3$ to $10^{-3} \, m^3$. Latent heat of water $= 2250 \, kJ/kg$.	$(P)$ $2 \, kJ$
$(II)$ $0.2 \, moles$ of a rigid diatomic ideal gas with volume $V$ at temperature $500 \, K$ undergoes an isobaric expansion to volume $3V$. Assume $R = 8.0 \, J \, mol^{-1} \, K^{-1}$.	$(Q)$ $7 \, kJ$
$(III)$ One mole of a monatomic ideal gas is compressed adiabatically from volume $V = 1/3 \, m^3$ and pressure $2 \, kPa$ to volume $V/8$.	$(R)$ $4 \, kJ$
$(IV)$ Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 \, kJ$ of heat and undergoes isobaric expansion.	$(S)$ $5 \, kJ$
	$(T)$ $3 \, kJ$

Which one of the following options is correct?

In the given $P-V$ diagram,a monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac{1}{3}\right)^{0.6} \simeq 0.5, \ln 2 \simeq 0.7$].
Which of the following statement$(s)$ is(are) correct?
$(A)$ The magnitude of the total work done in the process $A \rightarrow B \rightarrow C$ is $144 \text{ kJ}$.
$(B)$ The magnitude of the work done in the process $B \rightarrow C$ is $84 \text{ kJ}$.
$(C)$ The magnitude of the work done in the process $A \rightarrow B$ is $60 \text{ kJ}$.
$(D)$ The magnitude of the work done in the process $C \rightarrow A$ is zero.

One mole of a monatomic ideal gas undergoes the cyclic process $J \rightarrow K \rightarrow L \rightarrow M \rightarrow J$,as shown in the $P - T$ diagram. Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option. [$R$ is the gas constant]

$List-I$	$List-II$
$(P)$ Work done in the complete cyclic process	$(1)$ $R T_0 - 4 R T_0 \ln 2$
$(Q)$ Change in the internal energy of the gas in the process $JK$	$(2)$ $0$
$(R)$ Heat given to the gas in the process $KL$	$(3)$ $3 R T_0$
$(S)$ Change in the internal energy of the gas in the process $MJ$	$(4)$ $-2 R T_0 \ln 2$
	$(5)$ $-3 R T_0 \ln 2$

Consider the following volume-temperature $(V-T)$ diagram for the expansion of $5$ moles of an ideal monoatomic gas. Considering only $P-V$ work is involved,the total change in enthalpy (in Joule) for the transformation of state in the sequence $X \rightarrow Y \rightarrow Z$ is $\qquad$ [Use the given data: Molar heat capacity of the gas for the given temperature range,$C_{v,m} = 12 \ J \ K^{-1} \ mol^{-1}$ and gas constant,$R = 8.3 \ J \ K^{-1} \ mol^{-1}$]

Match the List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. Pressure varies inversely with volume of an ideal gas.	$I$. Adiabatic process
$B$. Heat absorbed goes partly to increase internal energy and partly to do work.	$II$. Isochoric process
$C$. Heat is neither absorbed nor released by a system.	$III$. Isothermal process
$D$. No work is done on or by a gas.	$IV$. Isobaric process

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ With the increase in the pressure of an ideal gas,the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason $(R) :$ In isothermal process,$PV =$ constant,while in adiabatic process $PV^\gamma =$ constant. Here $\gamma$ is the ratio of specific heats,$P$ is the pressure and $V$ is the volume of the ideal gas. In the light of the above statements,choose the correct answer from the options given below $:$

An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to $4$ times its initial volume $(V_0)$, then isobarically compressed to its original volume. Finally, the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

Match List-$I$ with List-$II$.

$A$. Isobaric	$I$. $\Delta Q = \Delta W$
$B$. Isochoric	$II$. $\Delta Q = \Delta U$
$C$. Adiabatic	$III$. $\Delta Q = 0$
$D$. Isothermal	$IV$. $\Delta Q = \Delta U + P \Delta V$

$\Delta Q = \text{Heat supplied}$,$\Delta W = \text{Work done by the system}$,$\Delta U = \text{Change in internal energy}$,$P = \text{Pressure of the system}$,$\Delta V = \text{Change in volume of the system}$. Choose the correct answer from the options given below:

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Isothermal	$(I)$ $\Delta W = 0$
$(B)$ Adiabatic	$(II)$ $\Delta Q = 0$
$(C)$ Isobaric	$(III)$ $\Delta U \neq 0$
$(D)$ Isochoric	$(IV)$ $\Delta U = 0$

Choose the correct answer from the options given below:

Two gases $A$ and $B$ are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$,respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure,the pistons of gas $A$ and $B$ are displaced by $16 \ cm$ and $9 \ cm$,respectively. If the change in their internal energy is the same,then the ratio $\frac{r_A}{r_B}$ is equal to

Column-$I$ shows graphs of thermodynamic processes, and column-$II$ contains information about various thermodynamic variables. Match column-$I$ with the information in column-$II$.

Column-$I$	Column-$II$
$(A)$ $PV$ vs $V$ (Isothermal expansion)	$(P)$ $W$ > 0
$(B)$ $P$ vs $T$ (Isochoric heating)	$(Q)$ $W$ < 0
$(C)$ $P$ vs $V$ (Isobaric expansion)	$(R)$ $\Delta Q$ > 0
$(D)$ $V$ vs $T$ (Isobaric compression)	$(S)$ $\Delta U$ > 0
	$(T)$ $\Delta U$ < 0

Match the following $:-$

Column-$I$	Column-$II$
$(i)$ Adiabatic process	$(a)$ Constant temperature
$(ii)$ Isolated system	$(b)$ No exchange of energy and matter
$(iii)$ Isothermal change	$(c)$ First law of thermodynamics
$(iv)$ Law of conservation of energy	$(d)$ No transfer of heat only

The molar heat capacity in a process of a diatomic gas,if it does a work of $\frac{Q}{4}$ when a heat of $Q$ is supplied to it,is

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of $1000 K$ is $0.4$. It extracts $150 J$ of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance $10$. The hot reservoir of the heat pump is at a temperature of $300 K$. Which of the following statements is/are correct:
$(A)$ Work extracted from the Carnot engine in one cycle is $60 J$.
$(B)$ Temperature of the cold reservoir of the Carnot engine is $600 K$.
$(C)$ Temperature of the cold reservoir of the heat pump is $270 K$.
$(D)$ Heat supplied to the hot reservoir of the heat pump in one cycle is $540 J$.

An ideal monatomic gas of $n$ moles is taken through a cycle $W-X-Y-Z-W$ consisting of consecutive adiabatic and isobaric quasi-static processes,as shown in the schematic $V-T$ diagram. The volumes of the gas at $W, X,$ and $Y$ points are $64 \ cm^3, 125 \ cm^3,$ and $250 \ cm^3,$ respectively. If the absolute temperature of the gas $T_W$ at point $W$ is such that $nRT_W = 1 \ J$ ($R$ is the universal gas constant),then the amount of heat absorbed (in $J$) by the gas along the path $XY$ is $.....$

One mole of a diatomic gas does a work $\frac{Q}{3}$,when the amount of heat supplied is $Q$. In this process,the molar heat capacity of the gas is:

$A$ monoatomic gas at pressure $P$,having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (Take $\gamma = 5/3$)

$A$ monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in increasing the internal energy and that used for doing external work is $A$ and $B$ respectively. Then the ratio,$A: B$ is

Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal rigid diatomic gas at $303 \ K$. The piston of cylinder $A$ is free to move,and that of cylinder $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder $B$ is $49 \ K$,then the rise in temperature of the gas in $A$ is: (in $K$)

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q: \Delta U: \Delta W$ is
[Given $\rightarrow \Delta Q=$ heat supplied,$\Delta U=$ change in internal energy,$\Delta W$ $=$ work done]

The internal energy of an ideal diatomic gas corresponding to volume $V$ and pressure $P$ is $2.5 PV$. The gas expands from $1 \text{ litre}$ to $2 \text{ litre}$ at a constant pressure of $10^5 \text{ N/m}^2$. The heat supplied to the gas is: (in $\text{ J}$)

The relation between efficiency $(\eta)$ of a Carnot engine and the coefficient of performance $(\beta)$ of a refrigerator working between the same temperatures is:

Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal diatomic gas at temperature $T$ $K$. The piston of cylinder $A$ is free to move,while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $dT_{A}$,then the rise in temperature of the gas in cylinder $B$ is (where $\gamma = \frac{C_{P}}{C_{V}}$):

If heat energy $\Delta Q$ is supplied to an ideal diatomic gas,the increase in internal energy is $\Delta U$ and the amount of work done by the gas is $\Delta W$. The ratio $\Delta W: \Delta U: \Delta Q$ is

The efficiency of a heat engine is $\eta$ and the coefficient of performance of a refrigerator is $\beta$. Then:

Three samples $X, Y$,and $Z$ of the same gas have equal volumes and temperatures. The volume of each sample is doubled. The process is isothermal for $X$,adiabatic for $Y$,and isobaric for $Z$. If the final pressures are equal for the three samples,find the ratio of the initial pressures. (Take adiabatic exponent $\gamma = 3/2$)

$A$ polyatomic gas at pressure $P$,having volume $V$ expands isothermally to a volume $3V$ and then adiabatically to a volume $24V$. The final pressure of the gas is (for a polyatomic gas,assume degrees of freedom $f = 6$,so $\gamma = 4/3$):

In the thermodynamic processes, which of the following statements is $NOT$ true?

There are two samples $A$ and $B$ of a certain gas,which are initially at the same temperature and pressure. Both are compressed from volume $V$ to $\frac{V}{2}$. Sample $A$ is compressed isothermally while sample $B$ is compressed adiabatically. The final pressure of $A$ is

Initial pressure and volume of a gas are $P$ and $V$ respectively. First,its volume is expanded to $4V$ by an isothermal process,and then its volume is reduced to $V$ by an adiabatic process. Find its final pressure if $\gamma = \frac{3}{2}$.

Two gases $A$ and $B$ have the same initial state $(P, V, n, T)$. Gas $A$ is compressed to $V/8$ by an isothermal process,and gas $B$ is compressed to $V/8$ by an adiabatic process. The ratio of the final pressure of gas $A$ to that of gas $B$ is (Both gases are monoatomic,$\gamma = 5/3$).