Question

A gas is heated in such a way that its pressure and volume both become double. Now by decreasing temperature, some of air molecules were introduced into the container to maintain the increased volume and pressure. Assuming ${\frac{1}{4}}^{th}$ of the initial number of moles has been given for this purpose. By what fraction of temperature has been raised finally of initial absolute temperature.

• A. $\frac{4}{5}$times
• B. $\frac{16}{7}$times
• C. $\frac{16}{5}$ times
• D. $\frac{8}{5}$ times

Answer 1

The correct option is C $\frac{16}{5}$ times

From combined gas law,
We know that,
$\frac{P_1{V}_1}{T_1}=\frac{P_2\times V_2}{T_2}$
Here, $P_2=2P_1$ and $V_2=2V_1$
So,
$\frac{P_1{V}_1}{T_1}=\frac{2P_1\times 2V_1}{T_2}$ and according to the given situation
$4T_1\times n_1=T_2^{\prime }{n}_2^{\prime }$...(at constant $PV$)
$T_2=4T_1$
$4T_1{n}_1=T_2^{\prime }\times \frac{5}{4}{n}_1(n_2=n_1+\frac{n_1}{4})$
& $\therefore T_2^{\prime }=\frac{16}{5}{T}_1$