Question

When a gas is compressed in an insulated vessel

• A. its internal energy decreases
• B. its temperature decreases
• C. both its pressure and volume increase
• D. both its temperature and volume increase
• E. both its temperature and internal energy increase

Hint:

In adiabatic compression, work done on the gas increases its internal energy, leading to a rise in temperature.

Answer 1

Answer: (E)

Step 1: Understand the meaning of insulated vessel.
An insulated vessel means no heat exchange with surroundings. Thus, the process is adiabatic: \[ Q=0 \]

Step 2: Apply the first law of thermodynamics.
\[ Q=\Delta U+W \] Since \(Q=0\), we get: \[ 0=\Delta U+W \] \[ \Delta U=-W \]

Step 3: Interpret work done during compression.
During compression, work is done on the gas. Therefore, work done by the gas is negative: \[ W<0 \] Thus, \[ \Delta U=-(-|W|)=+|W| \] So internal energy increases.

Step 4: Relate internal energy to temperature.
For an ideal gas, internal energy depends only on temperature: \[ U\propto T \] Hence, increase in internal energy means increase in temperature.

Step 5: Analyze volume and pressure.
During compression, volume decreases and pressure increases, so options involving increase in volume are incorrect.

Step 6: Identify the correct statement.
Since both temperature and internal energy increase, option (5) is correct.

Step 7: State the final answer.
\[ \boxed{\text{both its temperature and internal energy increase}} \] which matches option \((5)\).