One mole of diatomic ideal gas undergoes a cy | vedclass

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Question

(B) For a diatomic ideal gas,the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$.The change in internal energy $\Delta U$ for any proce

Vedclass · Accepted Answer

The change in internal energy in the process $BC$ is $-500\,R$.

Vedclass · Answer

(B) For a diatomic ideal gas,the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$.The change in internal energy $\Delta U$ for any process is given by $\Delta U = n C_V \Delta T$.$1$. For process $AB$ (isochoric): $\Delta U_{AB} = n C_V (T_B - T_A) = 1 	imes \frac{5}{2}R 	imes (800 - 400) = 1000\,R$.$2$. For process $BC$ (adiabatic): $\Delta U_{BC} = n C_V (T_C - T_B) = 1 	imes \frac{5}{2}R 	imes (600 - 800) = -500\,R$.$3$. For process $CA$ (isobaric): $\Delta U_{CA} = n C_V (T_A - T_C) = 1 	imes \frac{5}{2}R 	imes (400 - 600) = -500\,R$.$4$. For the whole cyclic process,the change in internal energy is $\Delta U_{total} = \Delta U_{AB} + \Delta U_{BC} + \Delta U_{CA} = 1000\,R - 500\,R - 500\,R = 0$.Comparing these results with the given options,option $B$ is correct.

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

One mole of diatomic ideal gas undergoes a cyclic process $ABC$ as shown in the figure. The process $BC$ is adiabatic. The temperatures at $A, B$,and $C$ are $400\,K, 800\,K$,and $600\,K$ respectively. Choose the correct statement.

Similar Questions

$A$ cyclic process $ABCDA$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?

An ideal gas is subjected to a cyclic process $A B C D$ as depicted in the $p-V$ diagram given below. Which of the following curves represents the equivalent cyclic process?

Which of the following is correct in terms of increasing work done for the same initial and final state?

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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