To solve this problem, we can use the following formula:
t = (m * c * ΔT) / P
where t is the time taken to warm the plasma to 90°, m is the mass of the plasma, c is the specific heat capacity of the plasma, ΔT is the change in temperature (90° - 40° = 50°), and P is the power of the oven.
We can assume that the mass and specific heat capacity of the plasma are constant.
If the oven is set at 100°, we have:
t = (m * c * ΔT) / P
t = (m * c * 50) / (100 - 40) (since P = 100 - 40 = 60)
t = (m * c * 50) / 60
t = (5m * c) / 6
If the oven is set at 140°, we have:
t = (m * c * ΔT) / P
t = (m * c * 50) / (140 - 40) (since P = 140 - 40 = 100)
t = (m * c * 50) / 100
t = (m * c) / 2
If the oven is set at 80°, we have:
t = (m * c * ΔT) / P
t = (m * c * 50) / (80 - 40) (since P = 80 - 40 = 40)
t = (m * c * 50) / 40
t = (5m * c) / 8
Therefore, it will take 5/6 times as long (or approximately 42.5 minutes) if the oven is set at 100°, half as long (or 22.5 minutes) if the oven is set at 140°, and 5/8 times as long (or approximately 28.1 minutes) if the oven is set at 80°, compared to the original time of 45 minutes when the plasma was placed in an oven at 120°.