Question

An ideal gas is compressed isothermally. During this process:

• A. Internal energy remains constant
• B. Temperature increases
• C. No work is done on the gas
• D. Pressure remains constant

Hint:

For an ideal gas: \[ \text{Internal Energy} \propto \text{Temperature} \] So in:
• Isothermal process: \( \Delta U = 0 \)
• Isochoric process: \( W = 0 \)
• Isobaric process: \( P = \text{constant} \)

Answer 1

The Correct Option is A

Concept: An isothermal process is a thermodynamic process in which the temperature remains constant throughout: \[ \Delta T = 0 \] For an ideal gas, internal energy depends only on temperature. Therefore: \[ \Delta U \propto \Delta T \] Hence, if temperature does not change, the internal energy also remains constant.

Step 1: Identify the nature of the thermodynamic process.
The gas is compressed isothermally, which means: \[ T = \text{constant} \] Therefore: \[ \Delta T = 0 \]

Step 2: Relate internal energy with temperature for an ideal gas.
For an ideal gas: \[ U = f(T) \] which means internal energy depends only on temperature. Since temperature remains unchanged during the process: \[ \Delta U = 0 \] Thus, the internal energy remains constant.

Step 3: Examine the remaining options.

• Temperature does not increase because the process is isothermal.
• Work is done on the gas during compression.
• Pressure does not remain constant during compression; it increases as volume decreases. Hence, the correct option is: \[ \boxed{\text{(A) Internal energy remains constant}} \]