Question

Two cylinders A and B contain equal amounts of diatomic gas at T K. Piston A is free to move (isobaric), B is fixed (isochoric). If rise in temp of A is $dT_{A}$ for same heat $Q$, rise in B is}

• A. $dT_{A}/2$
• B. $dT_{A}/\gamma$
• C. $\gamma dT_{A}$
• D. $2dT_{A}$

Hint:

For the same heat, the temperature rise is higher in isochoric processes because no work is done.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Heat given at constant pressure (A) and constant volume (B) results in different temperature increases.

Step 2: Key Formula or Approach:
\( Q_p = n C_p dT_A \) and \( Q_v = n C_v dT_B \).

Step 3: Detailed Explanation:
Given same amount of heat is supplied: \( Q_p = Q_v \).
\[ n C_p dT_A = n C_v dT_B \]
\[ dT_B = \left( \frac{C_p}{C_v} \right) dT_A \]
Using the definition of \( \gamma \):
\[ dT_B = \gamma dT_A \]

Step 4: Final Answer:
The temperature rise in B is \( \gamma dT_A \).