The internal energy ($U$), pressure ($P$) and volume ($V$) of an ideal gas are related as $\mathrm{U}=3 \mathrm{PV}+4$. The gas is:

(C) either mono-atomic or diatomic

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Heat & Thermodynamics

The internal energy (

U

), pressure (

P

) and volume (

V

) of an ideal gas are related as

U = 3 PV + 4

. The gas is:

(A)polyatomic only✓ Correct
(B)diatomic only
(C)either mono-atomic or diatomic
(D)mono-atomic only

Answer: (A)

Solution

For an ideal gas,

U = n C_{V} T

and

P V = n R T

. Given

U = 3 P V + 4

, ignoring the constant,

U \propto 3 P V

implies

n C_{V} T = 3 n R T

, so

C_{V} = 3 R

. For a polyatomic gas,

C_{V} = 3 R

(6 degrees of freedom). Therefore, the gas is polyatomic.

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Single correct option

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