Question

One mole of an ideal gas passes through a process where pressure and volume obey the relation P = Pₒ[1
- (Vₒ/V)².1/2]. Here Pₒ and Vₒ are constants. Calculate the change in the temperature of the gas if its volume change from Vₒ to 2Vₒ
(A) (1/4)(PₒVₒ/R)
(B) (1/2)(PₒVₒ/R)
(C) (5/4)(PₒVₒ/R)
(D) (3/4)(PₒVₒ/R)

Answer 1

Answer:

I think option C is correct

Answer 2

The change in the temperature of the gas if its volume change from Vₒ to 2Vₒ is ΔT = 5PoVo  / 4 nR

Option (C) is correct.

Explanation:

P = Po [ 1 - Vo^2/ 2v^2]

When Volume = Vo

Pressure = Po  [ 1 - Vo^2/ 2v^2] = Po/2

From ideal gas equation

PV = nRT

T1 = PoVo / 2nR

When volume = 2Vo

Pressure = Po [ 1 - Vo^2/ 8v^2] = 7Po /8

From PV = nRT

T2 = 7Po (2Vo) / 8 nR = 7PoVo / 4 nR

ΔT = T2 - T1  = PoVo / nR[ 7 / 4 - 1/2]

ΔT = 5PoVo  / 4 nR

Thus the change in the temperature of the gas if its volume change from Vₒ to 2Vₒ is ΔT = 5PoVo  / 4 nR