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
