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

Correct answer: B. polyatomic only U = 3PV + 4 (nf)/(2)RT = 3PV + 4 (f)/(2)PV = 3PV + 4 f = 6 + (8)/(PV) Since degree of freedom is more than 6 therefore gas is polyatomic

JEE Main 202126 FebruaryEvening Shift

Exam: JEE Main
Year: 2021
Date: 26 February
Shift: Evening Shift
Subject: Physics
Chapter: Thermodynamics

JEE Main 2021 · 26 February · Evening Shift · Physics · Thermodynamics

The internal energy (U) , pressure (P) and volume (V) of an ideal...

The internal energy

\left(U\right)

, pressure \left(P\right)

and volume \left(V\right)

of an ideal gas are related as

U = 3PV + 4 .

The gas is

Options

Aeither monoatomic or diatomic
Bpolyatomic only
Cmonoatomic only
Ddiatomic only

Correct answer

B. polyatomic only

Step-by-step solution

$U = 3PV + 4$
$\dfrac{nf}{2}RT = 3PV + 4$
$\dfrac{f}{2}PV = 3PV + 4$
$f = 6 + \dfrac{8}{PV}$
Since degree of freedom is more than $6$ therefore gas is polyatomic

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