Discussion
For an ideal gas, the specific heat at constant pressure is 1147 J/kg K and the ratio of specific heats is equal to 1.33. What is the value of the gas constant for this gas in J/kg K?
Answer: A
The gas constant is 284.6 J/kg K.
For an ideal gas \(R = c_{p} - c_{v}\) and \(\gamma = c_{p}/c_{v}\), so
\[ \begin{aligned} R &= c_{p}\left(1 - \frac{1}{\gamma}\right) = 1147 \times \frac{0.33}{1.33} \\ &= 284.6\ \text{J/kg K} \end{aligned} \]
862.4 J/kg K is \(c_{v} = 1147/1.33\), not \(R\). 1005 J/kg K is the usual \(c_{p}\) of air, a different gas from this one, and 8314 J/kmol K is the universal gas constant, which still has to be divided by the molar mass.
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