Question

Two systems have the following equations of state and are contained in a closed cylinder, separated by a fixed, adiabatic and impermeable piston. N1 = 2 and N2 = 1.5 moles. The initial temperatures are T1 = 175 K and T2 = 400 K. The total volume is 0.025 m3. The piston is allowed to move and heat transfer is allowed across the piston. Determine the final temperature of the system (in Kelvin).

Answer 1

The volumes of two systems are: V₁ and V₂.

From the given data:

V₁ + V₂ = V = 0.025 m³

Both systems are in a closed container in adiabatic condition, we have:

T₁ = 175 K

T₂ = 400 K

PV = nRT

nRT₁/P₁ + nRT₂/P₂ = nRT/P

2R×175/P + 1.5R×400/P = 3.5RT/P

2 × 175 + 1.5 × 400 = 3.5T

350 + 600 = 3.5T

950 = 3.5T

T = 950/3.5 = 271.42 K

Hence the final temeperature is 271.42 K.