Question

1.50 moles of an ideal monatomic gas are initially at a temperature of 317 K. If the gas gains 2730 J of heat and performs 780 J of work, what is its final temperature?

A) 756 K
B) 526 K
C) 687 K
D) 421 K
E) 359 K

Answer 1

The final temperature of the monatomic ideal gas after heat is gained and work is performed is 421.3 K, which rounds to 421 K (Option D).

Step-by-step explanation:

The question is about finding the final temperature of a monatomic ideal gas after it gains heat and performs work. Using the first law of thermodynamics, ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. For a monatomic ideal gas, the molar specific heat at constant volume, Cv, is (3/2)R, and the change in internal energy can be expressed as ΔU = nCvΔT. Therefore, ΔT = (Q - W) / (nCv). Substituting the given values, ΔT = (2730 J - 780 J) / (1.50 mol x (3/2)R). Assuming R = 8.314 J/(mol⋅K), ΔT = 1950 J / (1.50 mol x 12.471 J/K) = 104.3 K. Adding this to the initial temperature, the final temperature T2 = 317 K + 104.3 K = 421.3 K, which rounds to the closest offered answer, 421 K (Option D).