Calculating Change in Internal Energy for Compressed Air in a Closed System

In summary, the change in internal energy of a closed system is equal to the work done on the system.
  • #1
tommyhakinen
36
0

Homework Statement


10kg of air is compressed in a closed system from an initial temperature of 30° C to a final temperature of 260° C. Given cv = 710 J/kg.K.

Calculate the change in internal energy.

Homework Equations


ΔU = Q - W
W = P ΔV
Q = m c ΔT
P V = m R ΔT

The Attempt at a Solution


Since it is a compression, the work done is -ve. I am able to find the Q which has +ve since the temperature increases. However, how can I get the W?
 
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  • #2
tommyhakinen said:

Homework Statement


10kg of air is compressed in a closed system from an initial temperature of 30° C to a final temperature of 260° C. Given cv = 710 J/kg.K.

Calculate the change in internal energy.

Homework Equations


ΔU = Q - W
W = P ΔV
Q = m c ΔT
P V = m R ΔT

The Attempt at a Solution


Since it is a compression, the work done is -ve. I am able to find the Q which has +ve since the temperature increases. However, how can I get the W?

Be careful not to make the problem more complicated than it is.

From my reading of it, you have a closed system that has energy added to it in the form of work applied to compress the gas. No other energy goes in or comes out of the system. No other work is done to or by the system. Therefore, the change in energy of the system is equal to the work done on the system.

Make sense?
 
  • #3
So, you meant the change of internal energy ΔU = Q?
 
  • #4
tommyhakinen said:
So, you meant the change of internal energy ΔU = Q?

Yes. You have an energy input into the system (increase in internal energy), but no energy output (work done by the system).
 
  • #5
Ok. Got it now. So the key word in that problem is "closed system", right?
Okay. Thank you very much for the help..
 

1. What is thermodynamics?

Thermodynamics is the branch of physics that deals with the study of the relationship between heat, energy, and work. It explains how energy is transferred between different forms and how it can be used to do work.

2. What are the laws of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. The second law states that the total entropy of a closed system always increases over time. The third law states that as the temperature of a system approaches absolute zero, its entropy also approaches zero.

3. What is an example of a thermodynamic problem?

An example of a thermodynamic problem could be calculating the efficiency of an engine, which involves understanding the transfer of energy from heat to work. Other examples could include determining the heat capacity of a material or predicting the behavior of a chemical reaction under different temperature conditions.

4. How is thermodynamics applied in real life?

Thermodynamics has many practical applications in daily life, such as in the design of engines, refrigeration systems, and power plants. It is also used in the study of weather patterns, materials science, and chemical reactions.

5. What are the different branches of thermodynamics?

There are four main branches of thermodynamics: classical thermodynamics, statistical thermodynamics, chemical thermodynamics, and equilibrium thermodynamics. Classical thermodynamics deals with macroscopic systems and their energy exchanges, while statistical thermodynamics focuses on the behavior of microscopic particles. Chemical thermodynamics applies thermodynamic principles to chemical reactions, and equilibrium thermodynamics studies the behavior of systems in equilibrium.

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