Question

The volume of a gas at ${20}^{o}C$ is $100CC$ at normal pressure when it is heated to ${100}^{o}C$, its volume is $125CC$ at the same pressure the volume coefficient of the gas is

• A. ${\frac{1}{200}}^{o}C$
• B. ${\frac{1}{400}}^{o}C$
• C. ${\frac{1}{300}}^{o}C$
• D. ${\frac{1}{273}}^{o}C$

Answer 1

The correct option is C ${\frac{1}{300}}^{o}C$

Given: Volume of gas at ${20}^{o}C$ is 100 cc, and volume at ${100}^{o}C$ is 125 cc. Pressure is same throughout the process.

Solution:

Let, $v_i$ be the initial volume and $v_f$ be the final volume and $△T$ be the temperature difference.

$\therefore$ $△T=100-20={80}^{o}C$

We know that $v_f=v_i(1+\gamma △T)$, where $\gamma$ is volume coefficient of the gas.

Putting $v_i$=100, $v_f$=125, ${\triangle T}$=80, we get

125=100(1+80$\gamma )$

$\therefore \gamma =\frac{1}{320}$

The closest answer in the option is ${\frac{1}{300}}^{o}C$

Hence the correct option is C.