A gas expands from I to F in the figure.
The energy added to the gas by heat is 468 J
when the gas goes from I to F along the diagonal path.
P (atm)
4
3
2
1
0
F
Prev
X #1.
1$2
0
1
2
3
V (liters)
4
What is the change in internal energy of the gas?
Answer in units of J.
The change in internal energy of the gas is equal to the energy added to the gas by heat minus the work done by the gas during the expansion. In this case, the energy added to the gas by heat is 468 J.
To find the work done by the gas during the expansion, we can calculate the area under the curve of the path from I to F on the P-V diagram. Since the path is a diagonal line, the work done is equal to the area of a triangle.
First, we need to find the coordinates of points I and F on the P-V diagram.
Point I: (V=1 L, P=3 atm)
Point F: (V=3 L, P=1 atm)
The work done by the gas during the expansion is given by the formula:
Work = (1/2) * base * height
Work = (1/2) * (3-1) * (3-1)
Work = (1/2) * 2 * 2
Work = 2 J
Therefore, the change in internal energy of the gas is:
Change in internal energy = Energy added by heat - Work done by the gas
Change in internal energy = 468 J - 2 J
Change in internal energy = 466 J
Therefore, the change in internal energy of the gas is 466 J.