A rigid cubic box, 15 cm on a side, is filled with nitrogen gas (N₂) at standard temperature and pressure (0 °C and 1 atm). If 185 J of heat is added to the box, what is the final temperature of the gas?

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Quizplus · Accepted Answer

To find the final temperature of the gas after adding heat, we can use the formula $q = nC_{v}\Delta T$, where $q$ is the heat added, $n$ is the number of moles of gas, $C_{v}$ is the molar specific heat capacity at constant volume, and $\Delta T$ is the change in temperature. For nitrogen gas ($N_2$), $C_{v} = \frac{5}{2}R$, where $R = 8.314 \, \text{J/(mol·K)}$. At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.4 liters. The volume of the box is $15 \, \text{cm} \times 15 \, \text{cm} \times 15 \, \text{cm} = 3375 \, \text{cm}^3 = 3.375 \, \text{liters}$. Therefore, the number of moles of nitrogen gas in the box is $n = \frac{3.375}{22.4} \approx 0.151 \, \text{moles}$. Substituting the values into the formula, we get:$$185 = 0.151 \times \frac{5}{2} \times 8.314 \times \Delta T$$Solving for $\Delta T$, we find:$$\Delta T = \frac{185}{0.151 \times \frac{5}{2} \times 8.314} \approx 59 \, \text{K}$$Since the initial temperature was 0 °C (273 K), the final temperature is $273 + 59 = 332 \, \text{K}$, which is approximately 59 °C.

A Rigid Cubic Box, 15 Cm on a Side, Is