Question

The rise in temperature of an ideal gas $(\gamma =5/3)$ when at ${27}^{\circ }C$ it is adiabatically compressed to $8/27$ of its original volume is:

• A. $723K$
• B. $375K$
• C. $225K$
• D. $675K$

Answer 1

The correct option is B $375K$

For adibatic change, $T{V}^{\gamma -1}=constant$

$\therefore T_f{V}_f^{\gamma -1}=T_i{V}_i^{\gamma -1}$

Given, $V_f=\frac{8}{27}{V}_i$ and $T_i=273+27=300$ $K$

$\therefore T_f{\left(\frac{8}{27}\right)}^{\gamma -1}=300$

or, $T_f=300\times {\left(\frac{27}{8}\right)}^{2/3}$

$⟹T_f=300\times \frac{9}{4}$

$⟹T_f=675$ $K$

$\therefore$ Temperature rise $=675-300=375$ $K$