Question

Match the column with the correct numerical values of energy/heat in column-II (R is universal gas constant)

• A. A \( \rightarrow \) R; B \( \rightarrow \) P; C \( \rightarrow \) Q
• B. A \( \rightarrow \) P; B \( \rightarrow \) R; C \( \rightarrow \) Q
• C. A \( \rightarrow \) R; B \( \rightarrow \) Q; C \( \rightarrow \) P
• D. A \( \rightarrow \) Q; B \( \rightarrow \) P; C \( \rightarrow \) R

Hint:

For ideal gases, use the formulas for specific heat and internal energy to calculate the required quantities.

Answer 1

The Correct Option is A

Step 1: Calculate \( \Delta U \) for monatomic ideal gas.
For a monatomic ideal gas, \( \Delta U = \frac{3}{2} n R \Delta T \). For 1 mole and \( \Delta T = 320 \, \text{K} \), the heat change is 650 R. Step 2: Heat supplied to 2 moles of gas.
For 2 moles of gas with \( C = \frac{5}{2} R \), the heat supplied is \( Q = n C \Delta T = 800 R \). Step 3: \( \Delta U \) for diatomic gas.
For 1 mole of a diatomic gas with \( \Delta T = 230 \, \text{K} \), \( \Delta U = \frac{5}{2} R \Delta T = 480 R \). Final Answer: \[ \boxed{A \rightarrow R; B \rightarrow P; C \rightarrow Q} \]