What is an isochoric process and a cyclic process? Write the first law of thermodynamics for an ideal gas.
(N/A) $1$. Isochoric Process: A thermodynamic process in which the volume of the system remains constant $(dV = 0)$ is called an isochoric process. In this process, no work is done by or on the system $(W = 0)$.
$2$. Cyclic Process: A process is called cyclic if the system returns to its initial state after a series of changes. In a cyclic process, the change in internal energy is zero $(\Delta U = 0)$.
$3$. First Law of Thermodynamics: For an ideal gas, the first law of thermodynamics is given by $\Delta Q = \Delta U + \Delta W$, where $\Delta Q$ is the heat supplied to the system, $\Delta U$ is the change in internal energy, and $\Delta W$ is the work done by the system.
$2$. Cyclic Process: A process is called cyclic if the system returns to its initial state after a series of changes. In a cyclic process, the change in internal energy is zero $(\Delta U = 0)$.
$3$. First Law of Thermodynamics: For an ideal gas, the first law of thermodynamics is given by $\Delta Q = \Delta U + \Delta W$, where $\Delta Q$ is the heat supplied to the system, $\Delta U$ is the change in internal energy, and $\Delta W$ is the work done by the system.
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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
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View SolutionOne mole of a monoatomic gas and one mole of a diatomic gas are initially in the same state. Both gases are expanded isothermally and then adiabatically,such that they acquire the same final state. Choose the correct statement.
DifficultKVPY 2018
View SolutionThe 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 $ABCDA$
$(A)$ 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 $ABCDA$
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:
| $A$. 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:
One mole of an ideal monoatomic gas undergoes the following four reversible processes:
Step $1$: It is first compressed adiabatically from volume $8.0 \, m^{3}$ to $1.0 \, m^{3}$.
Step $2$: Then expanded isothermally at temperature $T_{1}$ to volume $10.0 \, m^{3}$.
Step $3$: Then expanded adiabatically to volume $80.0 \, m^{3}$.
Step $4$: Then compressed isothermally at temperature $T_{2}$ to volume $8.0 \, m^{3}$.
Then,$T_{1} / T_{2}$ is:
Step $1$: It is first compressed adiabatically from volume $8.0 \, m^{3}$ to $1.0 \, m^{3}$.
Step $2$: Then expanded isothermally at temperature $T_{1}$ to volume $10.0 \, m^{3}$.
Step $3$: Then expanded adiabatically to volume $80.0 \, m^{3}$.
Step $4$: Then compressed isothermally at temperature $T_{2}$ to volume $8.0 \, m^{3}$.
Then,$T_{1} / T_{2}$ is:
DifficultKVPY 2017
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