Five moles of an ideal monatomic gas with an initial temperature of 121 ∘C expand and, in the process, absorb an amount of heat equal to 1200 J and do an amount of work equal to 2020 J.

What is the final temperature of the gas?

T₂ ≈ 107.85∘C

Explanation:

The question didn't state if the volume is constant or not as such, we can apply the first law of thermodynamic

From the first law of thermodynamic,

ΔU = Q - W

where ΔU = Internal Energy, Q = Quantity of heat absorbed, W = Amount of work done.

Q = 1200 J and W = 2020 J

∴ ΔU = 1200 - 2020 = - 820 J.

Using the ideal gas equation,

ΔU = 3/2nRΔT ... equation 1

where n = number of moles, R = Molar gas constant, ΔT = Change in temperature = (T₂ - T₁).

Modifying equation 1,

ΔU = 3/2nR (T₂ - T₁) ... equation 2.

making T₂ the subject of the relation in equation 2,

T₂ = {2/3 (ΔU) / nR}+T₁ ... equation 3

where T₁=121∘C, R = 8.314 J / mol, n=5 moles, ΔU=-820 J

Substituting these values into equation 3,

∴ T₂ = { 2/3 (-820) / (5*8.314) }+121

T₂ = {2 * (-820) / (3*5*8.314) }+121

T₂={-1640/124.71} + 121

T₂ = {-13.151} + 121

∴T₂ = 121 - 13.151 = 107. 849∘C

T₂ ≈ 107.85∘C