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: Understanding the Concept:
The first law of thermodynamics says the change in internal energy equals heat absorbed plus work done on the system. An adiabatic process is one in which no heat is exchanged with the surroundings.

Step 2: Key Formula or Approach:
\[ \Delta U = Q + W \]
For an adiabatic process, \(Q = 0\).

Step 3: Detailed Explanation:
Put \(Q = 0\) into the first law:
\[ \Delta U = W \]
Multiply both sides by \(-1\):
\[ -\Delta U = -W \]
This is exactly option (B). Option (A), \(W = -Q\), would mean \(\Delta U = 0\), which describes an isothermal process of an ideal gas. Option (C) is not a valid statement of the first law. Option (D) is the general form at constant pressure with heat flowing, so it is not specific to adiabatic change.

Final Answer:
For an adiabatic process \(\Delta U = W\), which is written as \(-\Delta U = -W\) in option (B). \[ \boxed{-\Delta U = -W \text{ (B)}} \]