Adiabatic process definition

In an adiabatic process, there is no heat exchange between the system and surroundings: $dQ = 0$

First law of thermodynamics

The first law is: $dQ = dU + dW$ where:

• $dU$ = change in internal energy
• $dW$ = work done by the gas

For an adiabatic process: $0 = dU + dW$ so, $dU = -dW$

This means:

• if the gas does positive work, its internal energy decreases,
• if work is done on the gas, its internal energy increases.

Check each option

Option A: "The internal energy of the gas decreases as the temperature increases"

For an ideal gas, internal energy depends only on temperature. If temperature increases, internal energy increases, not decreases.

Hence, A is false.

Option B: "The molar heat capacity is zero"

Heat capacity for a process is defined as: $C = \frac{dQ}{dT}$ In an adiabatic process, $dQ = 0$ therefore, $C = 0$ provided temperature changes during the process.

Hence, B is true.

Option C: "Work done by the gas equals the increase in internal energy"

From $dU = -dW$ work done by the gas is equal to the decrease in internal energy, not the increase.

Hence, C is false.

Option D: "The molar heat capacity is infinite"

Infinite heat capacity corresponds to a process where temperature does not change despite heat exchange, such as an isothermal case in some contexts—not adiabatic.

Hence, D is false.

Final answer

The correct option is: $\boxed{\text{B}}$

Comparison with stored answer

Stored correct answer: B

My derived answer: B

They match.