One mole of an ideal gas with heat capacity at constant pressure Cp undergoes the process T-T0- V where T0 and - are constants- If its volume increases from V1 to V2- the amount of heat transfered to the gas is

From ideal gas equation, p=RTV=R(T_0+α V)V Work done by the gas W=∫_V_1^V_2p× dV=∫ _V_1^V_2R(T_0+α V)V× dV =RT_0lnV_2V_1+Rα (V_2 V_1) Change in internal energ ...

You visited us 11 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Degree of Freedom

One mole of a...

Question

One mole of an ideal gas with heat capacity at constant pressure $C_{p}$ undergoes the process $T = T_{0} + α V$ where $T_{0}$ and $α$ are constants. If its volume increases from $V_{1}$ to $V_{2}$ , the amount of heat transfered to the gas is

C_{p} R T_{0} ln \frac{V_{2}}{V_{1}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

α C_{p} (V_{2} - V_{1}) - R T_{0} ln \frac{V_{2}}{V_{1}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

α C_{p} (V_{2} - V_{1}) + R T_{0} ln \frac{V_{2}}{V_{1}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

R T_{0} \frac{V_{2}}{V_{1}} - α C_{p} (V_{2} - V_{1})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $α C_{p} (V_{2} - V_{1}) + R T_{0} ln \frac{V_{2}}{V_{1}}$
From ideal gas equation,
$p = \frac{R T}{V} = \frac{R (T_{0} + α V)}{V}$

Work done by the gas
$W = \int_{V_{1}}^{V_{2}} p \times d V = \int_{V_{1}}^{V_{2}} \frac{R (T_{0} + α V)}{V} \times d V$
$= R T_{0} ln \frac{V_{2}}{V_{1}} + R α (V_{2} - V_{1})$

Change in internal energy
$Δ U = n C_{V} Δ T$
$= (C_{p} - R) [(T_{0} + α V_{2}) - (T_{0} + α V_{1})]$
$= α (C_{p} - R) (V_{2} - V_{1})$

Hence, amount of heat transferred $Q = W + Δ U$
$= R T_{0} ln \frac{V_{2}}{V_{1}} + α C_{p} (V_{2} - V_{1})$

Suggest Corrections

Similar questions

Q. One mole of an ideal gas with heat capacity at constant pressure

C_{p}

undergoes the process

T = T_{0} + α V

, where

T_{0}

and

α

are constants, T is temperature and V is volume of the gas. The specific heat capacity of the gas as a function of its volume is: (if

C_{p}

and

C_{V}

denote specific heat at constant pressure and constant volume respectively)

Q. An ideal gas has a molar heat capacity

C_{v}

at constant volume. It undergoes a process given by

T = T_{0} e^{\frac{α}{V}}

, where

T_{0}

and

α

are constants. Find the molar heat capacity of the gas as a function of

V

Q. One mole of an ideal gas undergoes a process in which

T = T_{0} + a V^{3}

, where

T_{0}

and 'a' are positive constants and V is volume.
minimum pressure attainable is

Q. An ideal gas has a molar heat capacity

C_{v}

at constant volume. It undergoes a process given by

T = T_{0} e^{\frac{α}{V}}

, where

T_{0}

and

α

are constants. Find the molar heat capacity of the gas as a function of

V

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.

Join BYJU'S Learning Program

Explore more

Degree of Freedom

Standard XII Physics

Join BYJU'S Learning Program

One mole of an ideal gas with heat capacity at constant pressure Cp undergoes the process T=T0+αV where T0 and α are constants. If its volume increases from V1 to V2, the amount of heat transfered to the gas is

One mole of an ideal gas with heat capacity at constant pressure $C_{p}$ undergoes the process $T = T_{0} + α V$ where $T_{0}$ and $α$ are constants. If its volume increases from $V_{1}$ to $V_{2}$ , the amount of heat transfered to the gas is