AP EAMCET · PHYSICS · Kinetic Theory of Gases

A vessel has $6 g$ of oxygen at pressure $P$ and temperature $400 K$ . A small hole is made in it so that oxygen leaks out. How much oxygen leaks out if the final pressure is $\frac{P}{2}$ and temperature is $300 K$ ?

A $5 g$
B $4 g$
C $2 g$
D $3 g$

Verified Solution

Answer & Solution

Correct Answer

(C) $2 g$

Step-by-step Solution

Detailed explanation

From ideal gas equation, PV=nRT ⇒PV=mMRT ⇒P∝mT ⇒m∝PT ⇒m2m1=P2P1×T1T2 ⇒m2m1=P2P×400300 ⇒m2m1=23 Final mass, ⇒m2=23×m1=23×6 ⇒m2=4 g Leaked out mass =6-4=2 g

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A vessel has 6 g of oxygen at pressure P and temperature 400 K. A small hole is made in it so that oxygen leaks out. How much oxygen leaks out if the final pressure is P2 and temperature is 300 K?

Step-by-step Solution

A vessel has $6 g$ of oxygen at pressure $P$ and temperature $400 K$ . A small hole is made in it so that oxygen leaks out. How much oxygen leaks out if the final pressure is $\frac{P}{2}$ and temperature is $300 K$ ?