2.0 moles of an ideal monatomic gas are initially at a temperature of 300 K. If the gas gains 2800 J of heat and performs 400 J of work, what is its final temperature?

Question

Quizplus · Accepted Answer

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. For an ideal monatomic gas, the change in internal energy can also be expressed as ΔU = (3/2)nRΔT, where n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), and ΔT is the change in temperature. Given that 2.0 moles of gas gain 2800 J of heat and perform 400 J of work, the net heat added to the system is 2800 J - 400 J = 2400 J. Therefore, 2400 J = (3/2)(2.0 mol)(8.314 J/(mol·K))ΔT. Solving for ΔT gives a change in temperature of 96 K. Since the initial temperature was 300 K, the final temperature is 300 K + 96 K = 396 K.

20 Moles of an Ideal Monatomic Gas Are Initially at a Temperature