Question

Find increase in temperature for a gas when first its pressure and then volume both are doubled at \(400 \text{ K}\) .

• A. \(400 \text{ K}\)
• B. \(800 \text{ K}\)
• C. \(1200 \text{ K}\)
• D. \(1600 \text{ K}\)

Hint:

Doubling P and V → T becomes 4 times.

Answer 1

The Correct Option is C

Concept:
Ideal gas equation: \[ PV \propto T \]

Step 1: Initial temperature. \[ T_1 = 400 K \]

Step 2: Pressure doubled. \[ P \uparrow \Rightarrow T \uparrow (at constant V) \Rightarrow T = 800 K \]

Step 3: Volume doubled. \[ V \uparrow \Rightarrow T \uparrow (at constant P) \Rightarrow T = 1600 K \]

Step 4: Increase in temperature. \[ \Delta T = 1600 - 400 = 1200 K \]

Step 5: Conclusion. \[ \text{Increase = 1200 K} \]