Question

Heat supplied $dQ$ = increase in internal energy $dU$ is true for \dots

• A. isothermal process.
• B. adiabatic process.
• C. isobaric process.
• D. isochoric process.

Hint:

Learn the zeroes of thermodynamics:
- Isochoric: $dV = 0 \implies dW = 0 \implies dQ = dU$
- Isothermal: $dT = 0 \implies dU = 0 \implies dQ = dW$
- Adiabatic: $dQ = 0 \implies dU = -dW$

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks us to identify the specific thermodynamic process where the entire amount of heat supplied to a system goes directly into increasing its internal energy.

Step 2: Key Formula or Approach:
According to the First Law of Thermodynamics:
$$dQ = dU + dW$$
Where $dQ$ is heat supplied, $dU$ is the change in internal energy, and $dW$ is the work done by the gas.
Work done is defined as $dW = P \cdot dV$.

Step 3: Detailed Explanation:
The condition given is $dQ = dU$.
Substitute this into the First Law equation:
$$dU = dU + dW \implies dW = 0$$
Since $dW = P \cdot dV = 0$, this implies that the change in volume $dV$ must be zero (assuming pressure $P \neq 0$).
A process where volume remains strictly constant ($dV = 0$) is called an isochoric process (or isovolumetric process).
Because the gas cannot expand or contract, it does zero mechanical work, so 100% of the thermal energy injected simply heats the gas up, raising its internal energy.

Step 4: Final Answer:
This condition is true for an isochoric process, matching option (d).