Question

At a power plant that produces 1 GW (109 watts) of electricity, the steam turbines take in steam at a temperature of 500-C, and the waste heat is expelled into the environment at 20° C Suppose you develop a new material for making pipes and turbines, which allows the maximum steam temperature to be raised to 600°C. Roughly how much money can you make in a year by installing your improved hardware, if you sell the additional electricity for 5 cents per kilowatt-hour? (Assume that the amount of fuel consume d at the plant is unchanged.)

Answer 1

To calculate the money made by installing the improved hardware, we need to calculate the additional electrical energy produced due to the upgrade. The additional electrical energy produced is 8.3 GJ and the heat transfer to the environment decreases by 242 GJ. The additional money made in a year is $115,500.

Step-by-step explanation:

To calculate the money made by installing the improved hardware, we need to calculate the additional electrical energy produced due to the upgrade.

(a) The efficiency of the power station is 36%. With a 3.32% increase in efficiency, the new efficiency would be 36% + 3.32% = 39.32%. We can calculate the additional electrical energy produced as: (New efficiency - Old efficiency) * Heat transfer into the engine. Substituting the values, we get: (0.3932 - 0.36) * 2.50x10^14 J = 8.3x10^12 J = 8.3 GJ.

(b) The heat transfer to the environment can be calculated as: Heat transfer into the engine - Electrical energy produced. Substituting the values, we get: 2.50x10^14 J - 8.3x10^12 J = 2.42x10^14 J = 242 GJ.

To calculate the money made, we need to convert the additional electrical energy produced to kilowatt-hours and then multiply it by the selling price.

The additional electrical energy produced in kilowatt-hours is: (8.3x10^12 J / 3.6x10^6 J/kWh) = 2.31x10^6 kWh

The money made in a year is: (2.31x10^6 kWh) * ($0.05/kWh) = $115,500.