Net Force on Sides of Metal Box with Air at 1atm & 400K

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Homework Help Overview

The problem involves a sealed cubic metal box containing air, initially at a pressure of 1 atm and a temperature of 300 K, which is heated to 400 K. The inquiry focuses on determining the net force exerted on each side of the box due to the change in temperature and pressure of the air inside.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the ideal gas law and its implications for pressure changes as temperature increases. There are references to the relationship between pressure and force, as well as the need to consider the constants in the ideal gas law.

Discussion Status

Guidance has been offered regarding the use of the ideal gas law and the relationship between pressure and force. Participants are exploring the implications of constant volume and the number of particles in the box, indicating a productive direction in understanding the problem.

Contextual Notes

The discussion is framed within the constraints of a homework problem, with specific conditions regarding the sealed nature of the box and the temperatures involved. There is an emphasis on understanding the relationships between the variables rather than deriving a complete solution.

ice87
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A cubic metal box with sides of length 20cm contains air at pressure of 1atm and a temperature of 300K. The box is sealed so that the volume is constant and heated to 400K. What is the net force on each side of the box?

thanks dudes.
 
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Use PV=nRT
 
You'll also need the definition of pressure. It's a force divided by an area.
 
Yes, this is related to the ideal gas law (Pengwuino's formula), but really, all you need to know is the proportionality:

[tex]\frac{P_2}{P_1}=\frac{T_2}{T_1}[/tex]

To see why, consider that both before and after the gas is heated, it must satisfy the ideal gas law. Now, look at which variables are the same both before and after. Does the volume change? What about the number of particles in the box? Certainly the gas constant isn't going to change.

Once you determine the pressure, do you know the relationship between pressure and force?
 

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