# 0.5 mol of a monatomic gas reported an amount of heat Q = 5.5 kJ. In this case, the gas

0.5 mol of a monatomic gas reported an amount of heat Q = 5.5 kJ. In this case, the gas did the work A = 3800 J. Find the change in the internal energy of the gas? How much has the temperature changed as a result of this process?

According to the first law of thermodynamics, Q = ∆U + A ‘, ∆U = Q – A’ = 5500 J – 3800 J = 1700 J.

We got that part of the amount of heat went to the gas to do work, and the rest to change the internal energy. According to the formula ∆U = (3/2) νR∆T, we obtain the temperature change.

∆T = (∆U (2/3)) / νR = 1700 J x (2/3): (0.5 mol x 8.31 J / mol x K) ≈273K

Answer: ∆U = 1700 J, ∆T = 273K

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