First law of thermodynamics: A container with rigid walls is filled with 4 mol of air with C_V = 2.5R. How much does the internal (thermal) energy change if the temperature of the air rises from 16°C to 437°C? The ideal gas constant is R = 8.314 J/mol ∙ K.

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Quizplus · Accepted Answer

The change in internal energy ($\Delta U$) for an ideal gas can be calculated using the formula $\Delta U = nC_v\Delta T$, where $n$ is the number of moles, $C_v$ is the molar specific heat at constant volume, and $\Delta T$ is the change in temperature in Kelvin. Given $n = 4$ mol, $C_v = 2.5R$, and $R = 8.314$ J/mol∙K, and converting the temperature change from Celsius to Kelvin ($437°C - 16°C = 421K$), we get $\Delta U = 4 \times 2.5 \times 8.314 \times 421 = 35,000$ J or $35$ kJ.

First Law of Thermodynamics: a Container with Rigid Walls Is