Question

\(C_{p}\) and \(C_{v}\) are the specific heats at constant pressure and constant volume respectively. It is observed that \(C_{p}-C_{v}=a\) for hydrogen gas and \(C_{p}-C_{v}=b\) for carbon dioxide gas. The correct relationship between ' a' and 'b' is ( atomic weight of hydrogen , carbon and oxygen are 1u, 12 u and 16 u respectively)

• A. \(a=b\)
• B. \(a=22\ b\)
• C. \(a=44\ b\)
• D. \(a=\frac{1}{14b}\)

Hint:

For specific heats per unit mass, Mayer's relation is Cp minus Cv equals R divided by the molar mass.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Per mole, \(C_{p}-C_{v}=R\). For specific heats per unit mass, \(C_{p}-C_{v}=\frac{R}{M}\), where \(M\) is the molar mass.

Step 2: Calculation
Hydrogen: \(M=2\), so \(a=\frac{R}{2}\). Carbon dioxide: \(M=12+32=44\), so \(b=\frac{R}{44}\).

Step 3: Ratio
\(\frac{a}{b}=\frac{44}{2}=22\), so \(a=22\,b\).

Final Answer:
The relation between the two quantities is a equals 22 times b. \[ \boxed{\text{(B) }a=22\,b} \]