Question

Which of the following is/are correct \(Tds\) equation?

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

Hint:

Two important equations are \(Tds=C_VdT+T(\frac{\partial P}{\partial T})_VdV\) and \(Tds=C_PdT-T(\frac{\partial V}{\partial T})_PdP\).

Answer 1

The Correct Option is B

Concept:
The \(Tds\) equations are important thermodynamic relations connecting entropy, temperature, pressure and volume.

Step 1: First \(Tds\) relation.
One standard relation is: \[ Tds=C_VdT+T\left(\frac{\partial P}{\partial T}\right)_VdV \]

Step 2: Second \(Tds\) relation.
Another standard relation is: \[ Tds=C_PdT-T\left(\frac{\partial V}{\partial T}\right)_PdP \]

Step 3: Identify correct statements.
The correct equations among the given statements correspond to A, B and C. \[ A,B,C \text{ are correct} \] \[ D \text{ is incorrect} \]

Step 4: Final answer. \[ \therefore \text{Correct Answer is (B)} \]