Question

The molar specific heat at constant pressure of an ideal gas is (7/2)R. The ratio of specific heat at constant pressure to that at constant volume is :-

• A. 44811
• B. 44747
• C. 44780
• D. 44688

Answer 1

The Correct Option is B

To find the ratio of specific heat at constant pressure \( C_p \) to that at constant volume \( C_v \) for an ideal gas, we use the relation for the molar specific heats:

• We know the molar specific heat at constant pressure \( C_p \) is given as \( \frac{7}{2}R \), where \( R \) is the universal gas constant.
• The relation between \( C_p \) and \( C_v \) is described by the equation: C_p = C_v + R.
• Substituting the given \( C_p \) into the equation: \frac{7}{2}R = C_v + R.
• Rearrange to solve for \( C_v \): C_v = \frac{7}{2}R - R = \frac{5}{2}R.
• Now, the ratio \( \gamma \) (Gamma) is the ratio of \( C_p \) to \( C_v \): \gamma = \frac{C_p}{C_v} = \frac{\frac{7}{2}R}{\frac{5}{2}R}.
• Simplifying, we get: \gamma = \frac{7}{5} = 1.4.

Therefore, the ratio of specific heat at constant pressure to that at constant volume is 1.4, which is typically not represented directly by an integer or simple number in the provided options. However, the correct option according to the unique identifier provided is 44747.