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**[SOLVED]AP Question involving Ideal Gas Law - Thermal Physics - Pressure**

I am having some trouble with an old ap problem(PART C ONLY), see below:

## Homework Statement

1996 AP PHYSICS B Free Response Question:

The inside of the cylindrical can has a cross sectional area of 0.005 m^3 and length of 0.15 m. The can is filled with an ideal gas and covered with a loose cap. The gas is heated to 363 K and some is allowed to escape from the can so that the remaining gas reaches atmospheric pressure (1 x 10^5 Pa). The cap is now tightened, and the gas is cooled to 298 K.

a. What is the pressure of the cooled gas?

b. Determine the upward force exerted on the cap by the cooled gas inside the can.

c. If the cap develops a leak, how many moles of air would enter the can as it reaches a final equilibrium at 298 K and atmospheric pressure? (assume that air is an ideal gas)

## Homework Equations

P1/T1=P2/T2

P=F/A

PV=nRT

## The Attempt at a Solution

a) i figured this one out..

P1/T1=P2/T2

P2 = ~82093 Pascals

b) got this one too..

P = F/A

F = PA

F = ~410.5 Newtons

c) cannot get this one..

the volume of the gas that will enter into the leak is equal to the volume of the gas that escaped when the can was heated, correct? someone has said that this part will involve the volume of an ideal gas at STP, which is 22.4 Liters.

I am not sure what to do..

**Attempt at part c**- THIS IS INCORRECT, SEE BELOW FOR PROPER WORK

V1/T1=V2/T2

(0.005*0.15)/298=V2/363

V2= 9.136 x 10^-4 m^3

V2-V1 = V(escaped)

V(escaped) = 1.92 x 10^-4 m^3

PV(escaped)=nRT

n=PV(escaped)/RT

n= ((1x10^5)(1.92x10^-4)) / ((8.31)(298))

n= 0.0078 moles ??

Any help, explanations, and/or answers will be greatly appreciated.

Thank you!

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