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

[tommyhakinen]

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 c_v = 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?

 

[Stovebolt]

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 c_v = 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?

 

[tommyhakinen]

So, you meant the change of internal energy ΔU = Q?

 

[Stovebolt]

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).

 

[tommyhakinen]

Ok. Got it now. So the key word in that problem is "closed system", right?
Okay. Thank you very much for the help..