Does Room Temperature Affect Air Energy While Maintaining Constant Pressure?

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Homework Help Overview

The discussion revolves around the effects of temperature changes on the total energy of air in a room, specifically when the temperature is raised from 18 to 25 degrees Celsius while maintaining constant pressure. Participants are exploring the implications of the ideal gas law in this context.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants express differing views on whether total energy increases or remains constant with temperature changes. Some question the relationship between pressure and temperature, while others reference the ideal gas equation to explore how variables interact. There is a focus on understanding what must change to maintain the ideal gas law under the given conditions.

Discussion Status

The discussion is active, with participants presenting various interpretations of the ideal gas law and questioning assumptions about pressure and volume. Some guidance has been offered regarding the relationships between the variables, but no consensus has been reached on the implications for total energy.

Contextual Notes

Participants note that the room is not perfectly sealed, which may affect pressure and volume dynamics. There is an acknowledgment of the complexities involved in real-world scenarios versus idealized conditions.

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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?
 
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Grand said:

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
 
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.
 
Grand said:
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?
 
ok, then the volume of the air must also change so that the pressure can remain constant.
 
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
 
Wouldn't this equation be more for like a perfect case scenario where the room would be sealed off and not ventilated
 
Grand said:
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
 

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