Question

Find heat given to gas to take it from A to B. (Given: $C_v = 21$ S.I. units, $P_2 = 30$ Pa, $P_1 = 21.7$ Pa, $R = 8.3$ S.I. units, $n = 10$ moles) 

• A. $30$ J
• B. $21$ J
• C. $42$ J
• D. $50$ J

Hint:

For an isochoric process, work done is zero and heat supplied only changes internal energy.

Answer 1

The Correct Option is B

Step 1: Identifying the process.
From the $P$–$V$ diagram, the process from A to B is isochoric (constant volume).
Step 2: Heat given in isochoric process.
\[ Q = n C_v \Delta T \]
Step 3: Finding temperature change using ideal gas law.
\[ \Delta T = \dfrac{(P_2 - P_1)V}{nR} \]
Step 4: Substituting given values.
\[ Q = n C_v \dfrac{(P_2 - P_1)V}{nR} \]
\[ Q = \dfrac{21 (30 - 21.7)}{8.3} \]
Step 5: Final calculation.
\[ Q = 21 \text{ J} \]