A reversibel heat engine operates between thermal reserviors at 900K and 200K.If 9000J of heat is absorbed from the hot reserviors.
a.how much work is done by the heat engine?
b.What is the efficiency of the engine?
To answer these questions, we need to use the formula for the efficiency of a heat engine and the first law of thermodynamics.
a. The formula for the work done by a heat engine is:
Work = Heat input - Heat output
Since we are given that 9000J of heat is absorbed from the hot reservoir, the work done by the heat engine can be calculated as follows:
Work = 9000J
So, the work done by the heat engine is 9000J.
b. The efficiency of a heat engine is defined as the ratio of the work output to the heat input. The formula for efficiency is:
Efficiency = Work / Heat input
We have already found the work done by the heat engine, which is 9000J. The heat input can be calculated as the difference between the heat absorbed from the hot reservoir and the heat rejected to the cold reservoir:
Heat input = Heat absorbed - Heat rejected
Given that 9000J of heat is absorbed from the hot reservoir, we can calculate the heat rejected using the First Law of Thermodynamics:
Heat rejected = Heat absorbed - Work
Heat rejected = 9000J - 9000J
Heat rejected = 0J
Now, we can calculate the efficiency:
Efficiency = Work / Heat input
Efficiency = 9000J / (9000J - 0J)
Efficiency = 9000J / 9000J
Efficiency = 1
Therefore, the efficiency of the engine is 1, or 100%.