What is the amount of heat to heat a room?

[brainslush]

Homework Statement

A room was heated up during a time period ∆t. During this time period, temperature in the room increased from T1 to T2, while pressure remained unchanged and equal to pressure outside the building. Assuming that air may be considered as ideal gas, find an amount of heat Q spent to increase the internal energy of air in the room.

Homework Equations

The Attempt at a Solution

I assume that the room is not totally sealed thus some of the heated air leaks outside to keep the pressure inside the room equal to the pressure of the environment. So after a small heating T+dT there will be just n-dn number of molecules left in the room. It is less heat necessary to heat n-dn molecules than n molecules.
I have no idea how to put this into an equation. Please give me a hint.
I guess that this will be some kind of logarithmic function

 

[ojs]

Why do you suppose that matter has to leave the room? Can't the volume of the room change to keep the pressure constant? Else it would be way to difficult to calculate this since then you would have to heat up all the environment (or know the thermodynamical equilibrium of the room to the environment). Don't make that assumptions, rather just work with the ideal gas equation at constant mole number.