[一題廿分]Phy Q. about Gas Law

(a) Use the ideal gas equation: PV = nRT
or n = PV/RT

The no. of molesof gas initially in the gas cylinder, n0 = (1.5x10^6) x 0.3/RT
The no. of moles of gas in the balloon, ng = 10^5 x 1/RT
Hence, the no. of moles of gas left in the cylinder
= n0 - ng
= (1.5x10^6) x 0.3/RT - 10^5 x 1/RT

But (n0 - ng) = P'(0.3)/RT
where P' is the final pressure in the cylinder
Hence, P'(0.3)/RT = (1.5x10^6) x 0.3/RT - 10^5 x 1/RT
P' = (1.5x10^6 - 10^5/0.3) Pa = 1.167 x 10^6 Pa

(b) The final pressure in the cylinder will be 10^5 Pa, same as that in the balloons.
Let V be the max volume of balloon inflated.
since n0 = n0' + ng
where n0' is the number of moles of gas finally in the cylinder
(1.5x10^6) x 0.3/RT = 10^5 x 0.3/RT + 10^5 V/RT
(1.5x10^6) x 0.3 = 10^5 x 0.3 + 10^5 V
i.e. V = 4.2 m^3

We can use one formula for the 2 questions.

P1V1 = P2V2 where P stands for pressure and V stands for volume of the gas

a)

We consider the gas inside the cylinder,
before inflation,
the gas' volume is 0.3 m^3 under 1.5x10^6 Pa pressure
after inflation,
the gas' volume will be increase to 1+0.3 m^3

we get
( 1.5 x 10^6 )(0.3) = P x (1 + 0.3)

P will be the answer


b)
Again, we consider the gas inside the cylinder,
Assume the balloon is V m^3,
everything is the same as (a) but volume is unknown while pressure is given.

we get
( 1.5 x 10^6 )(0.3) = 10^5 x (N + 0.3)

N will be the answer