Ideal Gas Question Homework: Mass of Air in House @ 20C & -10C

[tiffanysnow]

Homework Statement

A house has a volume of 770 m^3. (a) what is the total mas of air inside the house at 20 Celsius? (b) If the temperature drops to -10 Celsius, what mass of air enters or leaves te house?

Homework Equations

PV = nRT

The Attempt at a Solution

I found the solution for part a which I think 924 kg. I found this answer by multiplying 770 m^3 by 1.2 kg (density of air at 20 Celsius: 1.2kg/m^3).
But I do not know how to find the answer to part b. I read the whole chapter but still did not know how. Please help me.

 

[rl.bhat]

Homework Statement

A house has a volume of 770 m^3. (a) what is the total mas of air inside the house at 20 Celsius? (b) If the temperature drops to -10 Celsius, what mass of air enters or leaves te house?

Using the formula
V₁T₁ = V₂/T₂
find V₂.
Then find the change in volume. Multiply it with density to get the mass air entering the room.

 

[tomcue]

Your solution for part a is correct. To find the answer for part b, we need to use the ideal gas law equation, PV = nRT. Since the volume of the house remains constant, we can set the two initial conditions equal to each other:
P1V1 = P2V2
where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume. We can also assume that the number of moles of air inside the house remains constant. This means that n1 = n2.
Rearranging the equation, we get:
n2 = (P1V1)/(RT2)
where T2 is the final temperature (-10 Celsius in this case).
We can substitute in the values for P1, V1, and T2 and solve for n2. Once we have the number of moles of air that enter or leave the house, we can use the molar mass of air (approximately 28.97 g/mol) to convert to mass in kilograms.
I hope this helps!