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CFSE Comparison

The molar spe...

Question

The molar specific heat of a gas as given from the kinetic theory is $\frac{5}{2} R$ . If it is not specified whether it is $C_{P}$ or $C_{V}$ , one could conclude that the molecules of the gas

A

Are definitely monoatomic

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B

Are definitely rigid diatomic

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C

Are definitely non-rigid diatomic

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D

Can be monoatomic or rigid diatomic

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Solution

The correct option is D Can be monoatomic or rigid diatomic
The value of $C_{P}$ is given as $(\frac{f}{2} + 1) R$
and that of $C_{V}$ is given as $(\frac{f}{2}) R$
Hence the possible values of $f$ for $C_{P}$ or $C_{V}$ to be $\frac{5}{2} R$ are $3, 5$ respectively.
The degrees of freedom for a monoatomic gas is $3$ .
The degrees of freedom for a rigid diatomic gas is $5$ .
Hence correct answer is option D.

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Similar questions

Q. For a rigid diatomic molecule, universal gas constant

R = n C p

^{'} C p^{'}

is the molar specific heat at constant pressure and

^{'} n^{'}

is a number. Hence

n

\frac{C_{p}}{C_{v}}

ratio for ideal gases with different types of molecules:

Column - I Molecule Type	Column -II $\frac{C_{p}}{C_{v}}$
$(A)$ Monatomic	$(I) \frac{7}{5}$
$(B)$ Diatomic rigid molecules	$(I I) \frac{9}{7}$
$(C)$ Diatomic non-rigid molecules	$(I I I) \frac{4}{3}$
$(D)$ Triatomic rigid molecules	$(I V) \frac{5}{3}$

Q. In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monoatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monoatomic gas are

C_{v} = \frac{3}{2} R, C_{p} = \frac{5}{2} R

and those for an ideal diatomic gas are

C_{v} = \frac{5}{2} R, C_{p} = \frac{7}{2} R

.
(where R is universal gas constant)

Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be

Q. Consider a mixture of

n

moles of helium gas and

2 n

moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its

\frac{C_{P}}{C_{v}}

Q. Assertion :The ratio of

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