Statement
5.6.3. The air in the room was heated from the temperature
time, the pressure did not change. Has the internal energy of the air inside
the room changed?
Solution
Assuming we're working with ideal gases
For an ideal gas, the internal energy only depends on the temperature
Careful here, we could think that obviously if the temperature increases, the internal energy increases too, but let's think this
We have
but this is only possible if n changed (air can escape), because if n is constant, the product nRT would vary with T, contradicting that PV is constant
So, from
and substituting this into the expression for the final energy
so
the internal energy did not change
Answer
The internal energy did not change