A gas expands from I to F in the figure.
The energy added to the gas by heat is 419 J
when the gas goes from I to F along the
diagonal path.
P (atm)
4
3
I A
2
1
B
F
0
+
01 2 3
4
V (liters)
What is the change in internal energy of the
gas?
Answer in units of J.

A gas expands from I to F in the figure The energy added to the gas by heat is 419 J when the gas goes from I to F along the diagonal path P atm 4 3 I A 2 1 B F class=


Answer :

Answer:

Part 1: 267 J

Part 2: 520 J

Explanation:

The first law of thermodynamics says that the sum of the heat and work that goes into a system must equal its change in internal energy. For a gas, work done is equal to -1 times the area under the curve on a P-v diagram. For part 1, the area is equal to the area of a trapezoid. For part 2, the area is a rectangle. We can use this to calculate the work done for each part, then find the missing variable.

Part 1 of 2

Work is equal to -1 times the area under the graph. For a trapezoid:

W = -½ (V₂ − V₁) (P₁ + P₂)

Plug in values (convert L to m³ and atm to Pa).

W = -½ (2.5 L − 1.5 L) (1 m³ / 1000 L) (0.5 atm + 2.5 atm) (101,325 Pa/atm)

W = -152 J

Notice the work is negative, meaning work is going out of the system. Given that 419 J of heat are going in, the change in internal energy is:

Q + W = ΔU

419 J − 152 J = ΔU

ΔU = 267 J

Part 2 of 2

This time, the area under the graph is a rectangle. The work done is therefore:

W = -(V₂ − V₁) P₁

W = -(2.5 L − 1.5 L) (1 m³ / 1000 L) (2.5 atm) (101,325 Pa/atm)

W = -253 J

For the same change in internal energy, the heat required is:

Q + W = ΔU

Q − 253 J = 267 J

Q = 520 J