(D) For a monoatomic gas, the molar heat capacity at constant volume is $C_v = \frac{3}{2}R$ and at constant pressure is $C_p = \frac{5}{2}R$. In cyli

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(D) For a monoatomic gas, the molar heat capacity at constant volume is $C_v = \frac{3}{2}R$ and at constant pressure is $C_p = \frac{5}{2}R$. In cylinder $B$, the piston is fixed, so the process is isochoric (constant volume). The heat supplied is $\Delta Q = n C_v \Delta T_B = n (\frac{3}{2}R) \Delta T_B$. In cylinder $A$, the piston is free to move, so the process is isobaric (constant pressure). The heat supplied is $\Delta Q = n C_p \Delta T_A = n (\frac{5}{2}R) \Delta T_A$. Since the heat supplied is the same in both cases, we have $n (\frac{3}{2}R) \Delta T_B = n (\frac{5}{2}R) \Delta T_A$. Given $\Delta T_A = 42 \,K$, we substitute the values: $\frac{3}{2} \Delta T_B = \frac{5}{2} \times 42$. $3 \Delta T_B = 5 \times 42 = 210$. $\Delta T_B = \frac{210}{3} = 70 \,K$.

Class 11 Physics Thermodynamics Mix Examples-Thermodynamics

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Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 \,K$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 \,K$, what is the rise in temperature of the gas in $B$ (in $\,K$)? (Given $\gamma = 5/3$)

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A
$25.2$
B
$35$
C
$42$
D
$70$

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An ideal gas expands isothermally from volume $V_1$ to volume $V_2$. It is then compressed to the original volume $V_1$ adiabatically. If $p_1$ and $p_2$ represent the initial pressure and final pressure respectively, and $W$ represents the net work done by the gas during the entire process, then:

MediumAP EAMCET 2010

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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.

DifficultIIT 2011

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Consider two containers $A$ and $B$ containing identical gases at the same pressure,volume and temperature. The gas in container $A$ is compressed to half of its original volume isothermally while the gas in container $B$ is compressed to half of its original volume adiabatically. The ratio of final pressure of gas in $B$ to that of gas in $A$ is

Medium

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$3$ moles of an ideal monoatomic gas performs an $ABCDA$ cyclic process as shown in the figure below. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J/mol \cdot K)$. (in $ \, kJ$)

DifficultTS EAMCET 2010

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An engine runs between a reservoir at temperature $200 \,K$ and a hot body which is initially at temperature of $600 \,K$. If the hot body cools down to a temperature of $400 \,K$ in the process,then the maximum amount of work that the engine can do (while working in a cycle) is (the heat capacity of the hot body is $1 \,J/K$).

KVPY 2020

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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.

Similar Questions

An ideal gas expands isothermally from volume $V_1$ to volume $V_2$. It is then compressed to the original volume $V_1$ adiabatically. If $p_1$ and $p_2$ represent the initial pressure and final pressure respectively, and $W$ represents the net work done by the gas during the entire process, then:

$3$ moles of an ideal monoatomic gas performs an $ABCDA$ cyclic process as shown in the figure below. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J/mol \cdot K)$. (in $ \, kJ$)

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