Question

Which of the following is the correct expression of the first law of thermodynamics for adiabatic processes ?

• A. \(W = -Q\)
• B. \(-\Delta U = -W\)
• C. \(\Delta U = QV\)
• D. \(\Delta U = Q_P-P_{\text{ext}}\,\Delta V\)

Hint:

In an adiabatic process Q = 0, so the first law gives delta U = W.

Answer 1

The Correct Option is B

Step 1: Start from the general law:
$\Delta U = q + w$, where $w$ is work done on the system.

Step 2: Apply the adiabatic condition:
Adiabatic means the system is thermally insulated, so $q = 0$. Then $\Delta U = w$.

Step 3: Match the options:
Negating both sides of $\Delta U = w$ gives $-\Delta U = -w$, which is option (B).
(A) $w = -q$ gives $\Delta U = 0$, which is true for an isothermal ideal gas, not an adiabatic change.
(C) $\Delta U = qV$ is not a recognised form of the law.
(D) keeps a heat term, so it cannot describe a process with no heat flow.

Final Answer:
Option (B) is the correct statement. \[ \boxed{-\Delta U = -W \text{ (B)}} \]