Solving Heat Radiation Problem: Max Work from N Identical Containers

In summary, the problem states that there are N identical containers, each with a volume of V and negligible heat capacity, filled with radiation at different temperatures (T1, T2, ..., Tn). The maximum work that can be extracted from these containers by operating reversible heat engines is given by the equation W_max=AV [∑(T_i)^4-N^(-1/3)*{∑(T_i)^3}^(4/3)], where i runs from 1 to n. The concept of entropy should be considered when attempting to solve this problem.
  • #1
neelakash
511
1

Homework Statement



N identical containers each of volume V and of negligible heat capacity are initially filled with radiations characteristic of temperatures T1,T2...Tn.Show that if no work or heat is available from other sources then by operating reversible heat engines between the containers,the maximum work that can be extracted is

W_max=AV [∑(T_i)^4-N^(-1/3)*{∑(T_i)^3}^(4/3)]

where i runs from 1 to n.

Homework Equations


The Attempt at a Solution



Please help me to start with this problem...I do not know LATEX...actually right now I do not have time to learn LATEX...

I am toally stuck at this.
 
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  • #2
Think entropy.
 

FAQ: Solving Heat Radiation Problem: Max Work from N Identical Containers

How can I calculate the maximum work from a given number of identical containers?

The maximum work from N identical containers can be calculated using the formula W = (N/2) * (kT), where N is the number of containers, k is the Boltzmann constant, and T is the temperature in Kelvin.

What is the significance of solving a heat radiation problem?

Solving a heat radiation problem is important in understanding the transfer of energy through radiation. This is crucial in various fields such as thermodynamics, engineering, and astrophysics.

Can the number of containers affect the maximum work obtained?

Yes, the number of containers directly affects the maximum work obtained. As the number of containers increases, the maximum work also increases. This is because there are more particles emitting and absorbing radiation, resulting in a higher transfer of energy.

Are there any limitations to the formula for calculating maximum work from identical containers?

Yes, the formula assumes that the containers are perfectly insulated and that there is no heat loss to the surroundings. In reality, this is not always the case, and the formula may need to be adjusted to account for these factors.

What are some real-life applications of solving a heat radiation problem?

Solving heat radiation problems has various applications, such as designing more efficient solar panels, understanding heat transfer in engines, and predicting the behavior of stars and other celestial bodies.

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