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
B
4g
C
2g
D
3g.

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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