Question

For an ideal gas, the specific heat at constant pressure is \(c_p = 1147 \ \mathrm{J\,kg^{-1}\,K^{-1}},\) and the ratio of specific heats is \(\gamma = 1.33.\)
What is the value of the gas constant \(R\) in \(\mathrm{J\,kg^{-1}\,K^{-1}}\)?
 

• A. 284.6
• B. 1005
• C. 862.4
• D. 8314

Hint:

Remember: \(R = c_p - c_v\) and \(\gamma = c_p/c_v\). If two of \(c_p, \gamma, R\) are known, the third can be found directly.

Answer 1

The Correct Option is A

Step 1: Relations among specific heats.
\[ \gamma = \frac{c_p}{c_v}, \qquad R = c_p - c_v. \] 

Step 2: Find \(c_v\).
\[ c_v = \frac{c_p}{\gamma} = \frac{1147}{1.33}. \] 

Compute: \[c_v \approx 862.4 \ \mathrm{J\,kg^{-1}\,K^{-1}} \]

Step 3: Find \(R\).
\[R = c_p - c_v = 1147 - 862.4 = 284.6 \ \mathrm{J\,kg^{-1}\,K^{-1}} \]

\[\boxed{284.6 \ \mathrm{J\,kg^{-1}\,K^{-1}}} \]