Thermodynamics-Finding Internal energy

AI Thread Summary
The discussion focuses on calculating internal energy and work in a Carnot cycle involving 0.5 kg of air. The highest and lowest temperatures in the cycle are determined to be 585.4 K and 292.7 K, respectively. The work done during the process is calculated as 107.5 kJ using the internal energy values. Participants seek clarification on how to find internal energy values u2 and u3, as well as the work done during isothermal processes. The efficiency of a Carnot cycle is also questioned, emphasizing the need for understanding thermodynamic principles.
tre2k3
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I am going over this example

0.5 kg of air undergoes a Carnot cycle with η = 0.5.
Given the initial pressure p1 = 700 kPa, initial
volume V1 = 0.12 m3 and heat transfer during the
isothermal expansion process Q12 = 40 kJ, Find
the highest and the lowest temperatures in the
cycle.
(b) the amount of heat rejection.
(c) work in each process.

They have Th to be 585.4k and Tl to be 292.7k
and so
W23 = m(u2 – u3)= 0.5(423.7 – 208.8) = 107.5 kJ

I do not know how to findu2 and u3. Looking at the tables at he back of the book doesn't help because they don't list the temperatures in this problem. So what equation is used to find u2 and u3 with the given information.
 
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