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NEET
Exam
NEET
Subject
Physics
Chapter
Kinetic Theory of Gases

NEET · Physics · Kinetic Theory of Gases

A rigid container is initially filled with oxygen gas. A student...

A rigid container is initially filled with oxygen gas. A student plots a pressure-temperature (P−TP-T) graph for the gas. The initial state of the gas is represented by point A at coordinates (T0,P0)(T_0, P_0). After some gas is allowed to leak out, the container is resealed and the gas reaches a new state represented by point B at coordinates (2T0,1.2P0)(2T_0, 1.2P_0). What percentage of the initial mass of the gas was released from the container?

Options

  1. A60%60\%
  2. B20%20\%
  3. C40%40\%
  4. D80%80\%

Correct answer

C. 40%40\%

Step-by-step solution

From the ideal gas equation, PV=nRT⇒n=PVRTPV = nRT \Rightarrow n = \dfrac{PV}{RT}.

For the initial state A, the number of moles is nA=P0VRT0n_A = \dfrac{P_0 V}{R T_0}.

For the final state B, the number of moles is nB=1.2P0VR(2T0)=0.6(P0VRT0)=0.6nAn_B = \dfrac{1.2 P_0 V}{R (2T_0)} = 0.6 \left(\dfrac{P_0 V}{R T_0}\right) = 0.6 n_A.

Since the mass of the gas is directly proportional to the number of moles, the remaining mass in the container is 60%60\% of the initial mass.

Therefore, the percentage of the initial mass that leaked out is 100%−60%=40%100\% - 60\% = 40\%.

Answer: 40%40\%
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