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(B) For a rigid diatomic gas,the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$ and at constant pressure is $C_P = \frac{7}{2}R$.In cy

Vedclass · Accepted Answer

$35$

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(B) For a rigid diatomic gas,the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$ and at constant pressure is $C_P = \frac{7}{2}R$.In cylinder $B$,the piston is fixed,so the process is isochoric (constant volume). The heat given is $Q = n C_V \Delta T_B$.Given $\Delta T_B = 49 \ K$,so $Q = n (\frac{5}{2}R) (49)$.In cylinder $A$,the piston is free to move,so the process is isobaric (constant pressure). The heat given is $Q = n C_P \Delta T_A$.Given $Q$ is the same,we have $n (\frac{5}{2}R) (49) = n (\frac{7}{2}R) \Delta T_A$.Canceling $n$,$R$,and the factor of $2$ from both sides: $5 	imes 49 = 7 	imes \Delta T_A$.$\Delta T_A = \frac{5 	imes 49}{7} = 5 	imes 7 = 35 \ K$.

Column-$I$	Column-$II$
$(a)$ Heat engine	$(i)$ $\text{COP} = \frac{Q_2}{Q_1 - Q_2}$
$(b)$ Heat pump	$(ii)$ $\eta = \frac{Q_1 - Q_2}{Q_1}$
	$(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$

Similar Questions

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$A$ monoatomic gas performs a work of $\frac{Q}{4}$,where $Q$ is the heat supplied to it. The molar heat capacity of the gas during this transformation will be $xR$,where $R$ is the gas constant. Find the value of $x$.

$A$ given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be $0.75$ of its initial pressure. The ratio of the specific heats of the gas is approximately:

One mole of an ideal gas having initial volume $V$,pressure $2P$ and temperature $T$ undergoes a cyclic process $ABCDA$ as shown below. The net work done in the complete cycle is:

Match the devices in Column-$I$ with their efficiency/coefficient of performance in Column-$II$:

Column-$I$ Column-$II$

$(a)$ Heat engine $(i)$ $\text{COP} = \frac{Q_2}{Q_1 - Q_2}$

$(b)$ Heat pump $(ii)$ $\eta = \frac{Q_1 - Q_2}{Q_1}$

$(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$

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