Question

Two cylinders each contain 0.20 mol of a diatomic gas at 250 K and a pressure of 3.0 atm. Cylinder A expands isothermally and cylinder B expands adiabatically until the pressure of each is 1.0 atm.

What is the final temperature of the gas in the cylinder A?

Express your answer to two significant figures and include the appropriate units.

What is the final volume of the gas in the cylinder A?

Express your answer to two significant figures and include the appropriate units.

What is the final volume of the gas in the cylinder B?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Cylinder A expands isothermally that means Temperature is constant.

Hence, PV = constant = k (let)

k = nRT => 0.20*0.0821*250 = 4.105

a. final temperature of the gas in the cylinder A would be same whichever initially was that is T2 = 250 K.

b.  final volume of the gas in the cylinder A would be:

PV = k

V = k/P => 4.105/1 = 4.105 l

Cylinder B expands adiabatically

final volume of the gas in the cylinder B would be:

Using V=nRT/P for before process,

V = k/P => 4.105/1 = 4.105 l

PV^gamma= constant

.i.e. PV^Y = k

Hence, 3*4.105^1.4 = 1*V^1.4

V^1.4 = 21.66

V = 2.157 l

Using again, PV = nRT

T = PV/nR => (1*2.157)/(0.20*0.0821) = 131.364 K