Heat funnction in steady state

In summary, the question posed is about the function that describes the surface temperature of a closed room with several identical machines that consume electrical energy and generate heat when turned on. It is assumed that the room is a ball for simplification purposes. The function is proportional to the power 3 of the number of machines that are turned on, as the surface area of a ball is proportional to the power 2 of its radius and the temperature is proportional to the heat generated by the machines.
  • #1
balulu
6
0
I was given the following interesting question.

A closed room contains several identical machines in it, they are fed by an electrical cable.
The machines can be turned on or off. When a machine is turned on, it consumes electrical energy and as a by product generates heat. The heat is radiated through the room walls to the outside air.
What is the function that describes the room surface temperature in steady state as a function of the number of machines that are turned on? Is it power 2 or 3 of β (the number of machines that are turned on)?

In order to simplify the analysis you can assume that the room is a ball.
 
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  • #2
The function would be proportional to the power 3 of β (the number of machines that are turned on), since the surface area of a ball is proportional to the power 2 of its radius and the temperature of the room surface is proportional to the heat generated by the machines.
 

Related to Heat funnction in steady state

1. What is the definition of a heat function in steady state?

A heat function in steady state refers to the thermal energy that is transferred between two systems in equilibrium, where the temperature of both systems remains constant over time.

2. How is the heat function calculated in steady state?

The heat function in steady state is calculated by taking the product of the heat transfer rate and the time interval over which the transfer occurs.

3. What factors affect the heat function in steady state?

The heat function in steady state is affected by the temperature difference between the two systems, the thermal conductivity of the materials involved, and the distance between the two systems.

4. What is the significance of heat function in steady state in real-world applications?

The heat function in steady state is important in many real-world applications, such as in the design of heating and cooling systems, and in thermodynamics processes.

5. How does the heat function in steady state differ from the heat function in transient state?

The heat function in steady state is a measure of the thermal energy transferred between two systems in equilibrium, while the heat function in transient state is a measure of the change in thermal energy over time as a system moves towards equilibrium.

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