An engine has a hot reservoir of 520K and a low temperature reservoir of 330K. What is the theoretical efficiency of this engine? Answer in units of %
Isn't this Carnot's Theorem?
http://en.wikipedia.org/wiki/Carnot_heat_engine
I used the theorem and got a answer of 37% but I don't think its right??
bhbhj
To calculate the theoretical efficiency of the engine, we can use the Carnot efficiency formula.
The Carnot efficiency is given by the equation:
Efficiency = 1 - (T_low / T_high)
Where:
- Efficiency is the efficiency of the engine (expressed as a decimal)
- T_low is the temperature of the low temperature reservoir (in Kelvin)
- T_high is the temperature of the high temperature reservoir (in Kelvin)
In this case, the high temperature reservoir has a temperature of 520K, and the low temperature reservoir has a temperature of 330K.
Plugging the values into the equation:
Efficiency = 1 - (330 / 520)
Calculating this expression gives us the following result:
Efficiency = 1 - 0.6346154
Simplifying further, we find:
Efficiency ≈ 0.3653846
To express this as a percentage, we can multiply the efficiency by 100:
Efficiency ≈ 0.3653846 * 100
Therefore, the theoretical efficiency of this engine is approximately 36.54%.