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Question

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 at $$\dfrac{P}{2}$$ and temperature $$300$$K?


A
5g
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B
4g
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C
2g
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D
3g.
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Solution

The correct option is C $$2$$g
$$PV=\dfrac{m}{M}RT$$(for m grams of gas)   .(i)
$$P'V=\dfrac{m'}{M}RT'$$       .(ii)
Dividing equation (ii) by (i) we get
$$\dfrac{P'}{P}=\dfrac{m'}{m}\dfrac{T;}{T}$$
$$m'=\dfrac{P'}{P}\times \dfrac{T}{T'}\times m=\left(\dfrac{P/2}{P}\right)\times \dfrac{400}{300}\times 6=4g$$
$$\therefore$$ Mass of oxygen leaked, $$\Delta m=m-m'=6-4=2g$$.

Physics

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