Molar heat capacities: An ideal monatomic gas cools from 455.0 K to 405.0 K at constant volume as 831 J of energy is removed from it. How many moles of gas are in the sample? The ideal gas constant is R = 8.314 J/mol ∙ K.

Question

Quizplus · Accepted Answer

The molar heat capacity at constant volume for a monatomic ideal gas is $C_V = \frac{3}{2}R$. The heat removed ($q$) is related to the temperature change ($\Delta T$) and the amount of substance ($n$) by the equation $q = nC_V\Delta T$. Rearranging for $n$, we get $n = \frac{q}{C_V\Delta T}$. Substituting the given values, $q = 831$ J, $R = 8.314$ J/mol·K, and $\Delta T = 455.0\,K - 405.0\,K = 50.0\,K$, we find $n = \frac{831}{\frac{3}{2} \times 8.314 \times 50} = 1.33$ mol.

Molar Heat Capacities: an Ideal Monatomic Gas Cools from 455