When the temperature of an enclosed gas is increased by 2 °C, its pre

1.	When the temperature of an enclosed gas is increased by 2 °C, its pressure increases by 0.5%. The initial temperature of the gas was(A) 250 K (B) 275 K (C) 300 K (D) 400 K.
Answer» Correct Option is (D) \(400^\circ C\) We know that , \(P \propto T\) \(\frac{P_1}{P_2} = \frac{T_1}{T_2}\) \(\frac{T_1}{T_2} = \frac{P_2}{P_1}\) \(\frac{P_2}{P_1} = \frac{T_2}{T_1}\) \(\because P_2 = P_1 + P_1 \times \frac{0.5}{100}\) \(P_2 = 1.005 P_1\) \(\frac{1.005 \ P_1}{P_1} = \frac{T_1 + 2}{T_1}\) \(1.005 T_1 = T_1 + 2\) \(0.005T_1 = 2\) \(T_1 = \frac{2000}{0.005}\) \(T_1 = 400^\circ C\) Correct option is (D) 400 K.

When the temperature of an enclosed gas is increased by 2 °C, its pressure increases by 0.5%. The initial temperature of the gas was(A) 250 K (B) 275 K (C) 300 K (D) 400 K.

Answer»

Correct Option is (D) \(400^\circ C\)

We know that ,

\(P \propto T\)

\(\frac{P_1}{P_2} = \frac{T_1}{T_2}\)

\(\frac{T_1}{T_2} = \frac{P_2}{P_1}\)

\(\frac{P_2}{P_1} = \frac{T_2}{T_1}\)

\(\because P_2 = P_1 + P_1 \times \frac{0.5}{100}\)

\(P_2 = 1.005 P_1\)

\(\frac{1.005 \ P_1}{P_1} = \frac{T_1 + 2}{T_1}\)

\(1.005 T_1 = T_1 + 2\)

\(0.005T_1 = 2\)

\(T_1 = \frac{2000}{0.005}\)

\(T_1 = 400^\circ C\)

Correct option is (D) 400 K.