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Standard XII

Chemistry

Heat Capacity

One mole of a...

Question

One mole of an ideal gas has an internal energy given by $U = U_{0} + 2 P V$ , where $P$ is the pressure and $V$ the volume of the gas. $U_{0}$ is a constant. This gas undergoes the quasi-static cyclic process $A B C D$ as shown in the U-V diagram. The molar heat capacity of the gas at constant pressure is

2 R

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3 R

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\frac{5}{2} R

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4 R

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Solution

The correct option is B $3 R$
$U = U_{0} + 2 P V = U_{0} + 2 n R T = U_{0} + n (2 R) T = \int n C_{V} d T$
Hence $C_{V} = 2 R$
$⟹ C_{P} = C_{V} + R = 3 R$

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One mole of an ideal gas has an internal energy given by U=U0+2PV, where P is the pressure and V the volume of the gas. U0 is a constant. This gas undergoes the quasi-static cyclic process ABCD as shown in the U-V diagram. The molar heat capacity of the gas at constant pressure is

The correct option is B 3RU=U0+2PV=U0+2nRT=U0+n(2R)T=∫nCVdTHence CV=2R⟹CP=CV+R=3R

The correct option is B $3 R$
$U = U_{0} + 2 P V = U_{0} + 2 n R T = U_{0} + n (2 R) T = \int n C_{V} d T$
Hence $C_{V} = 2 R$
$⟹ C_{P} = C_{V} + R = 3 R$