Question

A sample of gas has a volume of $V_i$ litre at temperature $t_1^{\circ }C$. When the temperature of the gas is changed to $t_2^{\circ }C$ at constant pressure, then the volume of the gas was found to increase by 10%. The percentage increase in temperature is :

• A. $10$
• B. $(10+\frac{2730}{t_1})$%
• C. $20$
• D. $(0.1+t_1^{-1})$%

Answer 1

The correct option is B $(10+\frac{2730}{t_1})$%

According to Charles’s law

$V\propto T$ at constant pressure.

So, a $10\%$ increase in volume will also increase $10\%$ temperature too.

Since temperature is in Kelvin scale. So $10\%$ increase in temperature in Celsius scale will be:

$10\%+\frac{273}{t_1}\times 10\%$ ( As $1^{0}C=273K$)

i.e. $=(10+\frac{2730}{t_1})\%$will be percentage increase in temperature.

Thus option B is correct.