(A) Initial state: $V_A = V_B = V$,$p_A = p_B = p$.For container $A$ (isothermal process): $p_A V_A = p_A^{\prime} V_A^{\prime}$.Given $V_A^{\prime} =

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(A) Initial state: $V_A = V_B = V$,$p_A = p_B = p$.For container $A$ (isothermal process): $p_A V_A = p_A^{\prime} V_A^{\prime}$.Given $V_A^{\prime} = V/2$,so $p V = p_A^{\prime} (V/2) \Rightarrow p_A^{\prime} = 2p$.For container $B$ (adiabatic process): $p_B V_B^{\gamma} = p_B^{\prime} (V_B^{\prime})^{\gamma}$.Given $V_B^{\prime} = V/2$,so $p V^{\gamma} = p_B^{\prime} (V/2)^{\gamma} \Rightarrow p_B^{\prime} = p \cdot 2^{\gamma}$.The ratio of final pressures is $\frac{p_B^{\prime}}{p_A^{\prime}} = \frac{p \cdot 2^{\gamma}}{2p} = 2^{\gamma-1}$.

Class 11 Physics Thermodynamics Mix Examples-Thermodynamics

Medium

Two containers $A$ and $B$ contain equal volumes of an identical gas at the same pressure and temperature. The gas in container $A$ is compressed to half its original volume isothermally,while the gas in container $B$ is compressed to half its original volume adiabatically. The ratio of the final pressure of gas in container $B$ to that of gas in container $A$ is

AP EAMCET 2021 All AP EAMCET

A
$(2)^{\gamma-1}$
B
$\left(\frac{1}{2}\right)^{\gamma-1}$
C
$\left(\frac{1}{1-\gamma}\right)^2$
D
$\left(\frac{1}{\gamma-1}\right)^2$

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$A$ thermodynamic cycle takes in heat energy at a high temperature and rejects energy at a lower temperature. If the amount of energy rejected at the low temperature is $3$ times the amount of work done by the cycle,the efficiency of the cycle is

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Three moles of an ideal gas $\left( {{C_P} = \frac{7}{2}R} \right)$ at pressure ${P_A}$ and temperature ${T_A}$ is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally, the gas is compressed at constant volume to its original pressure ${P_A}.$ The correct $P-V$ and $P-T$ diagrams indicating the process are

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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

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Two moles of helium gas are taken over the cycle $ABCDA$, as shown in the $P-T$ diagram. The net work done on the gas in the cycle $ABCDA$ is ...... $R$.

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$540$ calories of heat converts $1$ cubic centimeter of water at $100\,^oC$ into $1671$ cubic centimeter of steam at $100\,^oC$ at a pressure of one atmosphere. Then the work done against the atmospheric pressure is nearly .......... $cal$.

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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

Similar Questions

$A$ thermodynamic cycle takes in heat energy at a high temperature and rejects energy at a lower temperature. If the amount of energy rejected at the low temperature is $3$ times the amount of work done by the cycle,the efficiency of the cycle is

Two moles of helium gas are taken over the cycle $ABCDA$, as shown in the $P-T$ diagram. The net work done on the gas in the cycle $ABCDA$ is ...... $R$.

$540$ calories of heat converts $1$ cubic centimeter of water at $100\,^oC$ into $1671$ cubic centimeter of steam at $100\,^oC$ at a pressure of one atmosphere. Then the work done against the atmospheric pressure is nearly .......... $cal$.

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