An ideal diatomic gas - - 7-5 undergoes a process in which its internal energy relates to the volume as U - - -V- where - is a constant- Find the molar specific heat of the gas-

Given : #160;For diatomic gas #160; #160; γ #160; = 75 = 1.4 The process is #160; #160; #160; U #160;= α√(V) ∴ #160; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Heat Capacity

An ideal diat...

Question

An ideal diatomic gas $(γ = \frac{7}{5})$ undergoes a process in which its internal energy relates to the volume as $U = α \sqrt{V}$ , where $α$ is a constant. Find the molar specific heat of the gas.

Open in App

Solution

Given : For diatomic gas $γ = \frac{7}{5} = 1.4$
The process is $U = α \sqrt{V}$
$∴$ $\frac{f}{2} R T = α \sqrt{V}$
$⟹$ $T^{2} V^{- 1} = K = c o n s t a n t$
OR $T V^{- 1 / 2} = K^{'} = c o n s t a n t$
Comparing with $T V^{m - 1} = c o n s t a n t$ we get $m - 1 = - \frac{1}{2}$
$⟹ m = \frac{1}{2}$
$∴$ Molar heat capacity of the gas $C = \frac{R}{γ - 1} + \frac{R}{1 - m}$
$C = \frac{R}{1.4 - 1} + \frac{R}{1 - 0.5} = \frac{9}{2} R$

Suggest Corrections

Similar questions

An ideal gas, having ratio of specific heat

γ

undergoes a process in which its internal energy relates to the volume as

U = α \sqrt{V}

where

α

is a constant. If the gas is expanded from volume

V_{1} t o V_{2}

The work performed by gas is :

Q. An ideal diatomic gas

(γ = \frac{7}{5})

undergoes a process in which its internal energy relates to the volume as

U = α \sqrt{V}

, where

α

is a constant. If the work (in

J

) performed by the gas to increase its internal energy by

100 J

is 16k.Then what is the value of k?

An ideal diatomic gas under goes a process in which it internal energy changes with volume as given $U = c V^{\frac{2}{5}}$ where c is constant. Find the ratio of molar heat capacity of the process to universal gas constant R.___

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.

Q. An ideal monoatomic gas undergoes a process in which the gas volume relates to temperature as

V T = c o n s t a n t

. Then molar specific heat of gas in this process is:

Join BYJU'S Learning Program

An ideal diatomic gas (γ=75) undergoes a process in which its internal energy relates to the volume as U=α√V, where α is a constant. Find the molar specific heat of the gas.

Given : For diatomic gas γ=75=1.4The process is U=α√V∴ f2RT=α√V⟹ T2V−1=K=constantOR TV−1/2=K′=constantComparing with TVm−1=constant we get m−1=−12⟹m=12∴ Molar heat capacity of the gas C=Rγ−1+R1−m C=R1.4−1+R1−0.5=92R

An ideal diatomic gas $(γ = \frac{7}{5})$ undergoes a process in which its internal energy relates to the volume as $U = α \sqrt{V}$ , where $α$ is a constant. Find the molar specific heat of the gas.