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.
Carnot efficiency is given by:
Efficiency = 1 - (T_cold / T_hot)
Where:
Efficiency is given to be 39.0 percent or 0.39 (in decimal form).
T_cold is the temperature at which the engine exhausts heat, given as 46.0°C.
T_hot is the temperature at which the engine takes in heat (unknown).
We can rearrange the equation to solve for T_hot:
Efficiency = 1 - (T_cold / T_hot)
0.39 = 1 - (46.0 / T_hot)
Solving for T_hot, we can subtract 0.39 from both sides and then take the reciprocal of both sides:
0.39 = 1 - (46.0 / T_hot)
0.61 = 46.0 / T_hot
T_hot = 46.0 / 0.61
Calculating this gives us:
T_hot ≈ 75.41°C
Therefore, the minimum value of the temperature at which the engine takes in heat is approximately 75.41°C.