Two ideal gases A and B of same number of moles expand at constant temperatures T₁ and T₂ respectively such that the pressure of gas A decreases by 50 % and the pressure of gas B decreases by 75 % . If the work done by both the gases is same, then T₁: T₂

Step-by-step solution

Work done in isothermal process ( T = constant ) is aligned & W = nRT P ₁ P ₂ & ~W ₁= W ₂ nRT l ₁ ( P ₁ P ₂ )_ A = nRT ₂ ( P ₁ P ₂ )_ B & T ₁ ~T ₂ = ( P ₁ P ₂ )_ B ( P ₁ P ₂ )_ A = ( P ₁ 0.25 P ₁ ) ( P ₁ 0.5 P ₁ ) = 4 2 & = 2 2 2 = 2 1 =2: 1 aligned