Question

A volume of a gas at $ {{20}^{\circ}}C $ is $ 100\,c{{m}^{3}} $ at normal pressure. If it is heated to $ {{100}^{\circ}}C $ its volume becomes $125\, cm$ at the same pressure the volume coefficient of the gas will be normal pressure) :

• A. $ 0.0021{{/}^{o}}C $
• B. $ 0.0025{{/}^{o}}C $
• C. $ 0.0030{{/}^{o}}C $
• D. $ 0.0033{{/}^{o}}C $

Answer 1

Answer: (D)

The volume coefficient is given by
$ \alpha =\frac{{{V}_{2}}-{{V}_{1}}}{{{V}_{1}}{{T}_{2}}-{{V}_{2}}{{T}_{1}}} $
Given, $ {{T}_{1}}={{20}^{\circ}}C,$
${{V}_{1}}=100\,c{{m}^{3}},$
${{T}_{2}}={{100}^{\circ}}C $ ,
$ {{V}_{2}}=125\,\,c{{m}^{3}} $
$ \Rightarrow \alpha =\frac{125-100}{(100\times 100)-(125\times 20)} $
$ =\frac{25}{10000-2500} $
$ =\frac{75}{7500}=0.0033{{/}^{\circ}}C $ .