Question

Which of the following equations are correct?
\[ (A)\ U=H-PV \] \[ (B)\ G=H-TS \] \[ (C)\ U=q+W \]

• A. A, B and C
• B. A and B only
• C. A and C only
• D. B and C only

Hint:

Important thermodynamic relations: \[ H=U+PV \] \[ G=H-TS \] \[ \Delta U=q+w \] Always remember that the first law involves change in internal energy \(\Delta U\), not total internal energy \(U\).

Answer 1

The Correct Option is B

Step 1: Check equation (A).
We know that enthalpy is defined as \[ H=U+PV \] Rearranging, \[ U=H-PV \] Hence, equation (A) is correct.

Step 2: Check equation (B).
Gibbs free energy is defined as \[ G=H-TS \] where \[ H=\text{enthalpy}, \] \[ T=\text{temperature} \] and \[ S=\text{entropy} \] Therefore, equation (B) is also correct.

Step 3: Check equation (C).
According to the first law of thermodynamics, \[ \Delta U=q+w \] where \[ \Delta U \] represents the change in internal energy, not the total internal energy itself.
Thus, \[ U=q+W \] is incorrect because the correct relation should be \[ \Delta U=q+w \] Hence, equation (C) is incorrect.

Step 4: Final conclusion.
Therefore, the correct equations are \[ (A)\ \text{and}\ (B)\ \text{only} \] Hence, the correct answer is \[ \boxed{\text{A and B only}} \]