A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm³ to 150 cm³ adiabatically. In this process, the value of workdone on the gas will be :

<p>For monoatomic gas degree of freedom f = 3 and $\gamma$ = ${5 \over 3}$</p> <p>Here for gas,</p> <p>Initial pressure (P₁) = 75 kPa</p> <p>Initial volume (V₁) = 1200 cm³</p> <p>Final volume (V₂) = 150 cm³</p> <p>Final pressure (P₂) = ?</p> <p>For adiabatic process,</p> <p>${P_1}V_1^\gamma = {P_2}V_2^\gamma$</p> <p>$\Rightarrow 75 \times {(1200)^\gamma } = {P_2}{(150)^\gamma }$</p> <p>$$ \Rightarrow {P_2} = 75 \times {\left( {{{1200} \over {150}}} \right)^{{5 \over 3}}}$$</p> <p>$= 75 \times {(8)^{{5 \over 3}}}$</p> <p>$= 75 \times 32$ kPa</p> <p>= 2400 kPa</p> <p>Work done in adiabatic process,</p> <p>$W = {{{P_2}{V_2} - {P_1}{V_1}} \over {1 - \gamma }}$</p> <p>$$ = {{2400 \times {{10}^3} \times 150 \times {{10}^{ - 6}} - 75 \times {{10}^3} \times 1200 \times {{10}^{ - 6}}} \over {1 - {5 \over 3}}}$$</p> <p>$$ = {{(2400 \times 150 - 75 \times 1200) \times {{10}^{ - 3}}} \over { - {2 \over 3}}}$$</p> <p>$= {{ - 810000 \times {{10}^{ - 3}}} \over 2}$</p> <p>$= - 405$ kJ<p>