Question

A gas is compared adiabatically till its temperature is doubled. The ratio of his final volume to its initial volume will be :

• A. Between $\frac{3}{2}$ and 2.
• B. $\frac{1}{2}$
• C. More than $\frac{1}{2}$
• D. Less than $\frac{1}{2}$

Answer 1

Answer: (D)

Less than $\frac{1}{2}$

Using the relation,

$T_1{V}_1^{1-\gamma }=T_2{V}_2^{1-\gamma }$

$\frac{V_2}{V}={\left(\frac{T_1}{T_2}\right)}^{1-\gamma }={\left(\frac{T_1}{2T_2}\right)}^{1-\gamma }$

or $\frac{1}{(2{)}^{1-\gamma }}>\frac{1}{2}$