Question

The relation between U, P and V for an ideal gas is

U = 2 + 3 P V. The gas is –

• A. Monoatomic
• B. Diatomic
• C. Polyatomic
• D. Either a monoatomic or diatomic

Answer 1

Answer: (C)

Polyatomic

Answer 2

For an adiabatic process dQ = 0 = dU + dW

or 0 = dU + PdV

From the given equation

dU = 3 (PdV + VdP)

\ 0 = 3 (PdV + VdP) + PdV

or 4P (dV) + 3V (dP) = 0

or 4= – 3 $\left( \frac { \mathrm { dP } } { \mathrm { p } } \right)$

On integrating, we get

ln(V⁴) + ln(P³) = constant

or PV^4/3 = constant

i.e., g =$\frac { 4 } { 3 }$

i.e., gas is polyatomic.