An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation $P = k V$ . Molar heat capacity of the gas for the process is

C = C_{V} + R

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C = C_{V} + \frac{R}{2}

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C = C_{V} - \frac{R}{2}

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C = C_{V} + 2 R

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Solution

The correct option is A $C = C_{V} + \frac{R}{2}$
$P = k V \Rightarrow$
$P V^{- 1} = k$
It is polytropic process ( $P V^{n} =$ constant)
So $n = - 1$
So, $C = C_{V} + \frac{R}{1 - n} = C_{V} + \frac{R}{2}$

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Similar questions

Q. An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation P = kV. Show that the molar heat capacity of the gas for the process is given by

C = C_{V} + \frac{R}{2}

An ideal gas is taken through a process in which the pressure and the volume are chnaged according to the equation P = kV. Show that the molar heat capacity of the gas for the process is given by $C = C_{v} + \frac{R}{2}$ .

Q. An ideal gas has a molar heat capacity at constant volume

C_{V}

. Find the molar heat capacity of this gas as a function of its volume

V

, if it undergoes a process

T = T_{o} e^{α V^{2}}

, where

T_{o}

and

α

are constants.

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by $P V^{n}$ = constant, then n is given by (Here $C_{P}$ and $C_{V}$ are molar specific heat at constant pressure and constant volume, respectively):

For polytropic process $P V^{n} = c o n s t a n t, C_{m}$ (molar heat capacity) of an ideal gas is given by

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An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation P=kV. Molar heat capacity of the gas for the process is

The correct option is A C=CV+ R2P=kV⇒ PV−1=kIt is polytropic process (PVn=constant)So n=−1So, C=CV+ R1−n=CV+ R2

An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation $P = k V$ . Molar heat capacity of the gas for the process is

The correct option is A $C = C_{V} + \frac{R}{2}$
$P = k V \Rightarrow$
$P V^{- 1} = k$
It is polytropic process ( $P V^{n} =$ constant)
So $n = - 1$
So, $C = C_{V} + \frac{R}{1 - n} = C_{V} + \frac{R}{2}$