Question

Isotherms ($p$-$V$ lines) of one mole of an ideal gas at $T_1$ and $T_2$ have slope ratio 1:2. If $T_1=1000$ K, find $T_2$.

• A. 1000
• B. 2000
• C. 200
• D. 4000

Hint:

Slope of $p$-$V$ graph for isotherms $\propto$ temperature. Directly scale slope ratio with $T$.

Answer 1

The Correct Option is B

• For ideal gas, $pV = nRT \implies \text{slope of $p$ vs $V$ line} \propto T$.
• Slope ratio $T_1:T_2 = 1:2$.
• $T_2 = 2 \times 1000 = 2000$ K.