Question

One mole of an ideal gas (C_p / C_v) = γ at absolute temperature T₁ is adiabatically compressed from an initial pressure P₁ to a final pressure P₂ The resulting temperature T₂ of the gas is given by.

(A) T₂ = T₁ {p₂/ p₁}^{{γ/(γ–1)}} 

(B) T₂ =T₁ {p₂ / p₁}^{{(γ–1)/γ}}

(C) T₂ = T₁ {p₂ / p₁}^γ 

(D) T₂ = T₁ (p₂ / p₁)^γ–1

Answer 1

Correct option: (B) T₂ =T₁ {p₂ / p₁}^{{(γ–1)/γ}}

Explanation:

Adiabatic process hence PV^γ = constant

If n = 1 then PV = RT hence V = (RT / P)

∴ P(RT / P)^γ = constant

∴ P^(1–γ) ∙ T^γ = constant

 ∴ P^1–γ ∝ T^γ 

∴ (T₂ / T₁)^γ = (P₂ / P₁)^(1–γ) 

∴ (T₂ / T₁) = [(P₂ / P₁)^{(1–γ)×(1/γ)}]

T₂ =T₁ {p₂ / p₁}^{{(γ–1)/γ}}