Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V₂ = 2V₁ then ratio of temperature T₂/T₁ is: 

Concept:  

We know that for a polytropic process equation is given as:

PV^γ = K      -----(1)

Where P = pressure, V = volume, K = constant, γ = ratio of specific heats

PV = nRT ⇒ P = nRT/V      -----(2)

Calculations:

Given: 

Here, V2 = 2V₁ Then find T₂/ T₁ = ?

PV^1/2 = K where γ = 1/2 

From equation(1) and (2) we get:  nRT/V^1/2 = K      -----(3)

From equation (3) we get: T ∝ V^1/2       -----(4)

⇒T₂ / T₁ = (V₂ / V₁)^1/2     -----(4)

Put V2 = 2V1 in equation (4) we get:

T2 / T1 = (2V / V)1/2 = √2

Hence, option (2) is correct.