Convection equation thermodynamics

In summary, the problem asks how much the temperature of a concert hall, filled with 1800 people and with a volume of 2.2×104 m^3, would rise after 2.0 hours due to the metabolism of the people (70W/person), assuming no ventilation and an initial temperature of 293K. The approach to solving this problem may involve using the convection equation, but it is also possible that the problem simplifies the situation by assuming the whole room has one temperature and reaches equilibrium.
  • #1
yossup
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0

Homework Statement



An audience of 1800 fills a concert hall of volume 2.2×104 m^3. If there were no ventilation, by how much would the temperature of the air rise over a period of 2.0 h due to the metabolism of the people (70W/person)? Assume the room is initially at 293K.

Homework Equations





The Attempt at a Solution



I have no idea how to start this problem without using the convection equation...

can someone at least give me a hint on how to start this problem? this is so confusing...

thanks.
 
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  • #2
yossup said:
An audience of 1800 fills a concert hall of volume 2.2×104 m^3. If there were no ventilation, by how much would the temperature of the air rise over a period of 2.0 h due to the metabolism of the people (70W/person)? Assume the room is initially at 293K.
…
I have no idea how to start this problem without using the convection equation...

Hi yossup! :smile:

Yup … bit of a daft question, isn't it? :rolleyes:

My experience of daft exam questions tells me that since it says "the temperature", it means that you should assume that the whole room has only one temperature, and somehow reaches equilibrium! :wink:
 
  • #3


I would suggest starting by considering the principles of thermodynamics and how they apply to this situation. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred. In this case, the energy from the people's metabolism is being transferred to the air in the concert hall.

Next, you can use the convection equation, which relates the rate of heat transfer to the temperature difference between the two substances and their respective properties. In this case, the heat transfer is due to the metabolism of the people, and the substances are the air in the concert hall and the people themselves.

To solve the problem, you will need to calculate the amount of heat being transferred from the people to the air, and then use the convection equation to determine the temperature change over a period of 2.0 hours. You will also need to consider the specific heat capacity of air and the number of people in the concert hall.

I hope this helps you get started on solving the problem. Remember to always think critically and apply the relevant equations and principles to find a solution.
 

FAQ: Convection equation thermodynamics

What is the convection equation in thermodynamics?

The convection equation in thermodynamics is an equation that describes the transfer of heat through a fluid medium, such as air or water. It takes into account the temperature gradient, fluid velocity, and thermal conductivity of the medium. It is a fundamental equation in thermodynamics that is used to analyze heat transfer processes.

How is the convection equation different from the conduction equation?

The convection equation and the conduction equation are both used to describe heat transfer, but they differ in the way they model heat transfer. The conduction equation describes the transfer of heat through a solid medium, while the convection equation describes the transfer of heat through a fluid medium. Additionally, the convection equation takes into account the convective heat transfer coefficient, which is not a factor in the conduction equation.

What are the assumptions made in the convection equation?

There are several assumptions made in the convection equation, including: the fluid is incompressible, the flow is steady, the temperature gradient is constant, and the fluid properties are constant. These assumptions may not always hold true in real-world situations, but they are necessary for simplifying the equation and making it more manageable for analysis and calculations.

How is the convection equation used in practical applications?

The convection equation is used in a wide range of practical applications, including HVAC systems, refrigeration, and heat exchangers. It is also used in meteorology to model weather patterns and the Earth's climate. Additionally, the convection equation is used in the design of engines and turbines, as well as in the analysis of thermal insulation materials.

What are some limitations of the convection equation?

While the convection equation is a useful tool for analyzing heat transfer, it does have some limitations. One limitation is that it assumes a constant fluid velocity, which may not always be the case in real-world situations. Additionally, it does not take into account the effects of turbulence or boundary layer thickness, which can significantly impact heat transfer in certain scenarios. Therefore, it is important to carefully consider the assumptions and limitations of the convection equation when applying it to practical problems.

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