Question

If the temperature of an ideal gas is raised from \(T_1\) to \(T_2\) through the following processes, arrange the heat supplied in increasing order:
A. Adiabatic,
B. Isochoric,
C. Isobari
C.

• A. A \(<\) B \(<\) C
• B. B \(<\) A \(<\) C
• C. C \(<\) A \(<\) B
• D. A \(<\) C \(<\) B

Hint:

For the same rise in temperature, heat supplied is \(0\) in adiabatic, \(nC_V\Delta T\) in isochoric, and \(nC_P\Delta T\) in isobaric process.

Answer 1

The Correct Option is A

Concept:
For an ideal gas, heat supplied depends on the process.

Step 1: Adiabatic process.
In an adiabatic process: \[ Q=0 \] So, heat supplied is minimum. \[ A \text{ comes first} \]

Step 2: Isochoric process.
In an isochoric process: \[ Q=nC_V\Delta T \]

Step 3: Isobaric process.
In an isobaric process: \[ Q=nC_P\Delta T \] Since: \[ C_P>C_V \] therefore: \[ nC_P\Delta T>nC_V\Delta T \]

Step 4: Arrange in increasing order. \[ 0<nC_V\Delta T<nC_P\Delta T \] Thus, \[ A<B<C \] \[ \therefore \text{Correct Answer is (A)} \]