Question

The temperature of a definite amount of an ideal monoatomic gas becomes four times in a reversible process for which heat exchange is zero. Which of the following is correct relation between the final and initial parameters of gas?​

Answer 1

• The correct relation between the final and initial parameters of gas is Pf= 32 Pi.

Given-

Temperature becomes 4 times, so T₂ = 4 T₁

Heat exchange is zero, so Q = 0

Since, it is reversible process, so two equations are possible

(i) PV^γ = constant

(ii) TV^γ-1 = constant

From the second equation-

T₁V₁^γ-1 = T₂V₂^γ-1

Gas is mono atomic so, γ for mono atomic gas is 5/3

T₁V₁^2/3 = T₂V₂^2/3

T₂ = 4T₁

T₁V₁^2/3 = 4T₁V₂^2/3

V₁ = V₂ (4) ^ 3/2

V₁ = 8 V₂ or Vi = 8 Vf where Vi is V initial and Vf is V final.

From the first equation-

P₁V₁^γ = P₂V₂^γ

P₂ = P₁ (8)^5/3

P₂ = 32 P₁ or Pf = 32 Pi where Pf is P final and Pi is P initial.

Regards