Discussion
When a gas is compressed in an insulated vessel
Answer: E
Both its temperature and internal energy increase.
An insulated vessel allows no heat exchange, so the compression is adiabatic: \(Q = 0\). By the first law, \(\Delta U = Q + W_{\text{on}} = W_{\text{on}}\). Compressing the gas does positive work on it, so its internal energy rises, and for an ideal gas internal energy depends only on temperature, so the temperature rises too.
Internal energy and temperature therefore cannot decrease. In a compression the volume falls while the pressure rises, so 'both pressure and volume increase' and 'both temperature and volume increase' are both wrong.
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