For monoatomic gas degree of freedom f = 3 and $$\gamma$$ = $${5 \over 3}$$

Here for gas,

Initial pressure (P₁) = 75 kPa

Initial volume (V₁) = 1200 cm³

Final volume (V₂) = 150 cm³

Final pressure (P₂) = ?

For adiabatic process,

$${P_1}V_1^\gamma = {P_2}V_2^\gamma $$

$$ \Rightarrow 75 \times {(1200)^\gamma } = {P_2}{(150)^\gamma }$$

$$ \Rightarrow {P_2} = 75 \times {\left( {{{1200} \over {150}}} \right)^{{5 \over 3}}}$$

$$ = 75 \times {(8)^{{5 \over 3}}}$$

$$ = 75 \times 32$$ kPa

= 2400 kPa

Work done in adiabatic process,

$$W = {{{P_2}{V_2} - {P_1}{V_1}} \over {1 - \gamma }}$$

$$ = {{2400 \times {{10}^3} \times 150 \times {{10}^{ - 6}} - 75 \times {{10}^3} \times 1200 \times {{10}^{ - 6}}} \over {1 - {5 \over 3}}}$$

$$ = {{(2400 \times 150 - 75 \times 1200) \times {{10}^{ - 3}}} \over { - {2 \over 3}}}$$

$$ = {{ - 810000 \times {{10}^{ - 3}}} \over 2}$$

$$ = - 405$$ kJ