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We start with 5.00 moles of an ideal monatomic gas with an initial temperature of 128 ∘C. The gas expands and, in the process, absorbs an amount of heat equal to 1180 J and does an amount of work equal to 2020 J .
What is the final temperature of the gas?

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Answer:

The final temperature of the gas is 114.53°C.

Explanation:

Firstly, we calculate the change in internal energy, ΔU from the first law of thermodynamics:

ΔU=Q - W

ΔU = 1180 J - 2020 J = -840 J

Secondly, from the ideal gas law, we calculate the final temperature of the gas, using the change in internal energy:

[tex]ΔU=\frac{3}{2} nRΔT[/tex]

[tex]ΔU=\frac{3}{2} nR(T_{2} -T_{1} )[/tex]

Then we make the final temperature, T₂, subject of the formula:

[tex]T_{2} =\frac{2ΔU}{3nR} +T_{1}[/tex]

[tex]T_{2} =\frac{2(-840J)}{(3)(5)(8.314J/mol.K)} +128 deg.C[/tex]

[tex]T_{2} =114.53 deg.C[/tex]

Therefore the final temperature of the gas, T₂, is 114.53°C.

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