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0.25 mol of a gas are compressed at a constant pressure of 250 kPa from 6000 cm^3 to 2000 cm^3, then expanded at a constant temperature back to 6000 cm^3. What is the net work done on the gas?
22. The First Law of Thermodynamics
Cyclic Thermodynamic Processes
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An ideal gas is taken through the four processes shown below. The changes in internal energy for three of these processes are as follows: ΔEAB = +82 J; ΔEBC = +15 J; ΔEDA = –56 J. Find the change in internal energy for the process from C to D.
A
- 153 J
B
41 J
C
- 41 J
D
Cannot determine
Verified step by step guidance1
Understand that the problem involves an ideal gas undergoing a cyclic process, as depicted in the PV diagram. The cycle consists of four processes: AB, BC, CD, and DA.
Recall that for a cyclic process, the total change in internal energy over one complete cycle is zero. Therefore, the sum of changes in internal energy for all processes must equal zero: ΔEAB + ΔEBC + ΔECD + ΔEDA = 0.
Substitute the given values into the equation: ΔEAB = +82 J, ΔEBC = +15 J, and ΔEDA = -56 J. The equation becomes: 82 J + 15 J + ΔECD - 56 J = 0.
Solve for ΔECD by rearranging the equation: ΔECD = - (82 J + 15 J - 56 J).
Calculate the expression to find the change in internal energy for the process from C to D, which will give you the value of ΔECD.
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