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Question

The relation between U,P and V for an ideal gas is $$U=2+3PV$$. the gas is 


A
Monoatomic
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B
Diatomic
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C
Polyatomic
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D
Either a Monoatomic or Diatomic
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Solution

The correct option is C Polyatomic
Given:
U = 2+ 3PV
$$\Rightarrow U = 2+ 3 nRT$$
Differentiating with respect to T,
$$\Rightarrow \dfrac{dU}{dT} = 0+ 3nR\dfrac{dT}{dT}$$
$$\Rightarrow C_v = 3nR$$
For 1 mole of a gas, n=1
$$\Rightarrow C_v =3R$$
Since the specific heat at constant volume is 3R for triatomic gas in which atoms are non linear,
Therefore, correct option is C( polyatomic).

Physics

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