Question

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

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

Solution

## The correct option is C PolyatomicGiven: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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