Two different fuels are being considered for a 2.5 mw (net output) heat engine which can operate between the highest temperature produced during the burning of the fuels and an atmospheric temperature of 300 k. fuel a burns at 2,500 k, delivering 50 mj/kg (heating value) and costs $2.00/kg. fuel b burns at 1,500 k, delivering 40 mj/kg and costs $1.50/kg.

compare the fuel costs per hour of fuel a and fuel b, assuming that the heat engine operates
(a) at carnot efficiency
(b) at 40% of carnot efficiency

If the heat engine operates for one hour:

a) the fuel cost at Carnot efficiency for fuel 1 is $409.09 while fuel 2 is $421.88.

b) the fuel cost at 40% of Carnot efficiency for fuel 1 is $1022.73 while fuel 2 is $1054.68.

In both cases the total cost of using fuel 1 is minor, therefore it is recommended to use this fuel over fuel 2. The final observation is that fuel 1 is cheaper.

Explanation:

The Carnot efficiency is obtained as:

Where is the atmospheric temperature and is the maximum burn temperature.

For the case (B), the efficiency we will use is:

The work done by the engine can be calculated as:

where Hv is the heat value.

If the average net power of the engine is work over time, considering a net power of 2.5MW for 1 hour (3600s), we can calculate the mass of fuel used in each case.

If we want to calculate the total fuel cost, we only have to multiply the fuel mass with the cost per kilogram.