Question

Which of the following statements are correct for curves on \(T-S\) diagram?
A. The slope of an isochoric curve on \(T-S\) diagram is \(\frac{C_V}{T}\),
B. The slope of an isochoric curve on \(T-S\) diagram is \(\frac{T}{C_V}\),
C. The slope of an isobaric curve on \(T-S\) diagram is \(\frac{T}{C_P}\),
D. The slope of an isobaric curve on \(T-S\) diagram is \(C_P\), E. An isochoric curve has a greater slope than an isobaric curve on \(T-S\) diagram.

• A. B, C and E Only
• B. B and C Only
• C. A and B Only
• D. A, D and E Only

Hint:

On a \(T-S\) diagram, isochoric slope is \(\frac{T}{C_V}\) and isobaric slope is \(\frac{T}{C_P}\).

Answer 1

The Correct Option is A

Concept:
On a \(T-S\) diagram, the slope is: \[ \frac{dT}{dS} \] For reversible heat transfer: \[ dQ=T\,dS \]

Step 1: Isochoric curve.
For constant volume: \[ dQ=C_VdT \] Also: \[ dQ=T\,dS \] So, \[ T\,dS=C_VdT \] \[ \frac{dT}{dS}=\frac{T}{C_V} \] Thus, \[ B \text{ is correct} \]

Step 2: Isobaric curve.
For constant pressure: \[ dQ=C_PdT \] \[ T\,dS=C_PdT \] \[ \frac{dT}{dS}=\frac{T}{C_P} \] Thus, \[ C \text{ is correct} \]

Step 3: Compare slopes.
Since: \[ C_P>C_V \] therefore: \[ \frac{T}{C_V}>\frac{T}{C_P} \] So, an isochoric curve has greater slope than an isobaric curve. \[ E \text{ is correct} \] Thus, correct statements are: \[ B,C,E \] \[ \therefore \text{Correct Answer is (A)} \]