Question

One cylinder contains 0.1 mol of an ideal monatomic gas at a pressure of 1.0x105 Pa with a volume of 2.5x10-3 m3. Assuming that the gas expands to three times its initial volume, it determines the final gas temperature if the expansion is adiabatic.

Answer 1

The final temperature is T₂ =14,66 K

Explanation:

A relation for a process of abdicative expansion of an ideal gas is given by the following expression:

TV^(γ-1) = ctte -----> T₁V₁^(γ-1) = T₂V₂^(γ-1) .:. We calculate variable T1

For the calculation of the initial temperature (T1) we use the ideal gas equation:

PV = nRT

Data:

R = 0,082 kJ/kgK

V1 = 2,5x10^-3 m^3

P1 = 1x10^5 Pa

n = 0,1 mol

If we clear T1

T1 = P1V1/nR

T1 = 100Kpa * 2,5x10^-3 m^3 / 0,1 mol * 0,082 kJ/kgK

T1 = 30,49 K .:. We substitute this value in the initial equation:

T₁V₁^(γ-1) = T₂V₂^(γ-1) .:. We clear T2

T₂ = T₁V₁^(γ-1) / V₂^(γ-1)

γ = 5/3 (gas monatomic)

T₂ = 30,49 K (2,5x10^-3 m^3)^(5/3-1) / (3*2,5x10^-3 m^3)^(5/3-1)

T₂ =14,66 K