The maximum possible efficiency of a heat engine which exhaust its heat at a temperature of 46.0o is 39.0 percent. What is the minimum value of the temperature at which the engine takes in heat? (in oC).

To find the minimum value of the temperature at which the engine takes in heat, we can use the Carnot efficiency formula. The Carnot efficiency (η) of a heat engine is given by the formula:

η = 1 - (Tc/Th)

Where:
η is the efficiency of the heat engine
Tc is the temperature at which the engine exhausts its heat
Th is the temperature at which the engine takes in heat

We are given that the maximum possible efficiency (η) of the heat engine is 39.0% or 0.390. The temperature at which the engine exhausts its heat (Tc) is 46.0°C.

Substituting these values into the formula, we get:

0.390 = 1 - (46.0/Th)

To find the minimum value of Th, we rearrange the equation:

0.390 + 46.0/Th = 1

46.0/Th = 1 - 0.390

46.0/Th = 0.610

Now we can solve for Th by isolating it:

Th = 46.0 / 0.610

Th ≈ 75.41°C

Therefore, the minimum value of the temperature at which the engine takes in heat is approximately 75.41°C.