(A) Let the initial volume be $V_1 = V$ and the final volume be $V_2 = V/2$.In a $P-V$ diagram,the work done during a compression process is represent

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Compressing the gas through adiabatic process will require more work to be done.

(A) Let the initial volume be $V_1 = V$ and the final volume be $V_2 = V/2$.In a $P-V$ diagram,the work done during a compression process is represented by the area under the curve.For a given change in volume,the adiabatic curve is steeper than the isothermal curve.Since the adiabatic curve lies above the isothermal curve for the same volume range during compression,the area under the adiabatic curve is greater than the area under the isothermal curve.Therefore,compressing the gas through an adiabatic process requires more work to be done than compressing it isothermally.

Class 11 Physics Thermodynamics Mix Examples-Thermodynamics

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$A$ gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then

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A
Compressing the gas through adiabatic process will require more work to be done.
B
Compressing the gas isothermally or adiabatically will require the same amount of work.
C
Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.
D
Compressing the gas isothermally will require more work to be done.

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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 $\text{ J}$)

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An ideal monoatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2V$, the final pressure is $P_a$. The ratio $\frac{P_a}{P_i}$ is

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

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An ideal monoatomic gas is taken through a process $dQ = 2dU$. The molar heat capacity for the process is:

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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.

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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.

$A$ gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then

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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 $\text{ J}$)

An ideal monoatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2V$, the final pressure is $P_a$. The ratio $\frac{P_a}{P_i}$ is

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

An ideal monoatomic gas is taken through a process $dQ = 2dU$. The molar heat capacity for the process is:

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