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,$R = 8.3 \ J \ K^{-1} \ mol^{-1}$]
- A$8020$
- B$8030$
- C$8220$
- D$8120$
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$A$ cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in the figure. Find the heat exchanged by the engine with the surroundings for each section of the cycle. Given ${C_v} = \frac{3}{2}R$.
$(a)$ $A$ to $B$: constant volume
$(b)$ $B$ to $C$: constant pressure
$(c)$ $C$ to $D$: adiabatic
$(d)$ $D$ to $A$: constant pressure
$(a)$ $A$ to $B$: constant volume
$(b)$ $B$ to $C$: constant pressure
$(c)$ $C$ to $D$: adiabatic
$(d)$ $D$ to $A$: constant pressure
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View SolutionOne mole of a gas expands such that its volume $V$ changes with absolute temperature $T$ in accordance with the relation $V = K T^2$,where $K$ is a constant. If the temperature of the gas changes by $60 \text{ K}$,then the work done by the gas is ($R$ is the universal gas constant).
An insulating cylinder contains $4 \text{ moles}$ of an ideal diatomic gas. When a heat $Q$ is supplied to it,$2 \text{ moles}$ of the gas molecules dissociate. If the temperature of the gas remains constant,then the value of $Q$ is ($R$ - universal gas constant).
$A$ 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 $\gamma = 4/3$):
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: $P \quad Q \quad R \quad S$
| 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: $P \quad Q \quad R \quad S$
DifficultIIT 2013
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