Does Room Temperature Affect Air Energy While Maintaining Constant Pressure?

[Grand]

Homework Statement

The temperature in a room is raised from 18 to 25 C. They ask what happens with the total energy if the air in the room.

Homework Equations

The Attempt at a Solution

I say that it increases, but the answer is that it stays the same, because the pressure stays the same (I don't agree, because pressure depends on temperature) and therefore the total energy stays the same. Why is that?

 

[Andrew Mason]

Homework Statement

The temperature in a room is raised from 18 to 25 C. They ask what happens with the total energy if the air in the room.

Homework Equations

The Attempt at a Solution

I say that it increases, but the answer is that it stays the same, because the pressure stays the same (I don't agree, because pressure depends on temperature) and therefore the total energy stays the same. Why is that?

If the temperature goes up, pressure stays the same and volume remains the same, what must change? (hint: what is the only other variable in the ideal gas equation?). How does that affect the total energy in the room?

AM

 

[Grand]

Well, as far as I know, the ideal gas eq is
PV=nRT
and you mentioned all the variables in it in your post. If T goes up and the volume is obviously fixed, then pressure P should definitely go up.

Regards.

 

[Adjuster]

Well, as far as I know, the ideal gas eq is
PV=nRT
and you mentioned all the variables in it in your post. If T goes up and the volume is obviously fixed, then pressure P should definitely go up.

Regards.

The volume of the room is constant, but unless we plan to suffocate the room cannot be perfectly sealed. Provided that there is some ventilation, the pressure P can remain the same as the room is heated. What then changes apart from T?

 

[Grand]

ok, then the volume of the air must also change so that the pressure can remain constant.

 

[sigmaro]

It stays same, because total energy of all gas molecules are NkT=nN(avagadro)kT=nRT right? this is the start point of PV=nRT. pressure is more or less same for a room if it changes we can't breathe properly. Volume of the room is already constant. so left hand side of the equality is constant so must be right hand side of it which implies total energy is same. But it is like a dilemma. When you heat the gas, it will "expand" and some of the gas will leak out, so there will be less gas in room with higher energy but total energy of them equals to initial state in which there were more gas molecules wit lower energy

 

[dreit]

Wouldn't this equation be more for like a perfect case scenario where the room would be sealed off and not ventilated

 

[Andrew Mason]

ok, then the volume of the air must also change so that the pressure can remain constant.

Ideal gas equation: PV=nRT. Given: P, V, and R are constant. T changes. Question: What must change in order to preserve the ideal gas equation?

AM