Question

Calculate the change in internal energy of a gas if a gas is compressed adiabatically from 25 dm³ to 15 dm³ at constant external pressure of 4 bar.

Options

• 30 dm³ bar

• 40 dm³ bar

• 50 dm³ bar

• 56 dm³ bar

Answer 1

40 dm³ bar

Explanation:

\[\mathrm{P_{ext}=4~bar,~V_1=25~dm^3,~V_2=15~dm^3}\]
\[\Delta\mathrm{U}=\mathrm{Q}+\mathrm{W}=\mathrm{Q}-\mathrm{P}_\mathrm{ext}\Delta\mathrm{V}\]
For adiabatic process, Q = 0.
\[\therefore\quad\Delta\mathrm{U}=-\mathrm{P}_{\mathrm{ext}}\Delta\mathrm{V}\]
\[=-\mathrm{P}_{\mathrm{ext}}\left(\mathrm{V}_2-\mathrm{V}_1\right)\]
\[=-4\left(15-25\right)\]
\[=40\mathrm{dm}^3\mathrm{bar}\]