How Long for Air Pressure to Drop 30% in Space Capsule with a Hole?

[Valour549]

Air pressure drop in Space (please help!)

Homework Statement

A space capsule, which may be treated as a sphere of radius 10 m, is hit by a micrometeorite which makes a hole of diameter 2mm in its skin. Estimate how long it will take for the air pressure to drop by 30%. (Answer should be something like 26 days as a hint).

Homework Equations

Q= v A (Q flow rate, v velocity, A area)
PV = n R T or N k T (P pressure, V volume, n is moles, R gas constant, T temperate, N actual no. of molecules, k Boltzmaan's constant)

The Attempt at a Solution

V = 4188.8 m^3 (sphere's volume), A = 3.14 x 10^-6 m^2 (circle's area)

-I think it has something to do with the above equations, though I'm not entirely sure. Perhaps something to do with Fick's Laws of effusion/diffusion too?

-I think the pressure outside the capsule is zero at all times, so we'll just have to care only about the pressure inside due to the air inside the capsule

-From above, P = N/V * k * T, but pressure changes as air molecules escape (so now time is involved in the equation too), and I'm not sure how to deal with that. Furthermore, what do we put for temperate (absolute zero outside and room temp. inside initially, but that would change pretty fast)?

 

[chrisk]

Consider what values of the ideal gas law are constant with respect to time and those that are changing with time. The hint implies a slow leak so therefore the temperature can be considered constant. Once the constants and variables are determined take the time derivative of the ideal gas equation. This is a start to solving the problem.