Question

The specific heat of a gas is found to be $0.075$ calories at constant volume and its formula $wt$ is $40$. The atomicity of the gas would be:

• A. one
• B. two
• C. three
• D. four

Answer 1

Answer: (A)

one

Specific heat of gas is defined as the amount of heat required to raise the temperature of 1 g of substance by 1 K.

Given: $C_V=0.075cal/g/K$. Therefore $0.075cal$ is absorbed by 1 g of the gas at constant volume.

Formula wt of gas is 40 g. So total heat absorbed by the gas is:

$C_V=40\times 0.075=3cal/K/mol$.

Since , $C_p-C_V=R$ and $R=1.987cal/K/mol$

$\therefore C_p=C_V+R=3+1.987\approx 5$

Calculating $C_p/C_V=5/3=1.66$

Hence the gas is monatomic. Therefore option A is correct.