Two moles of a confined ideal monatomic gas begin at state A on the pressure-volume graph and follow the path shown to state D.If the temperature of the gas at A is 54 K,what is the temperature of the gas at D?

Question

Quizplus · Accepted Answer

Since the gas is ideal and monatomic, we can use the ideal gas law and the fact that the internal energy of an ideal monatomic gas is only dependent on temperature to solve the problem. From state A to state D, the gas follows a path of constant pressure followed by a path of constant volume. Thus, we can use the combined gas law to find the final temperature:

P_A V_A / T_A = P_D V_D / T_D

Since the moles and pressure do not change, we can simplify this equation to:

V_A / T_A = V_D / T_D

Substituting in the given values, we get:

8 L / 54 K = 2 L / T_D

Solving for T_D, we get:

T_D = (2 L × 54 K) / 8 L = 54 K

Therefore, the temperature of the gas at state D is also 54 K. Hence, the correct choice is (C).

Two Moles of a Confined Ideal Monatomic Gas Begin at State