will be very thankful renewable sources when they are available, and subsequent

Question

will be very thankful

renewable sources when they are available, and subsequent expansion of the air to drive turbines when demand for electricity is high. A facility in Huntorf, Germany pressurizes 0.3 million m of air in an underground cavern to a pressure of 40 atmospheres. Assume (as a simplification) that the compression is isothermal; and that when the air is expanded to drive a turbine, the conversion to electricity occurs with 50% efficiency. a. What is the total work done to compress the air? (Use the ideal gas law.) b. What is the total electrical energy delivered? How does this compare with the published value for Huntorf of 290,000 kW power delivered for 2 h?

Explanation / Answer

P1=1 atm ( 101325 Pascal), V1= 0.3X106 m3, P2= 40 atm

PV=nRT => 101325X0.3X106 = nRT

For an isothermal process, P1V1= P2V2 => V2/V1=P1/P2 = 1/40

Work done on the air W = nRT ln[Vf/Vi] = nRTln[P1/P2] = 101325X0.3X106 ln [1/40] = 112133X106 Joules

Thus work done to compress the air = 112133X106 Joules

b. Since efficiency is 50%, only 50% of this energy can be converted back into electrical energy. THus the total electrical energy delivered would be = 50/100 * 112133 X 106 = 56066.4 X106 J = 5.60664 x 1010 J

Now 290000 kW for 2h = 290000X103X2 X 60X 60 Joules ( converting hours to seconds)

= 208800 x 107 J = 2.088 x 1012 J

Published Value / Calculated Value = 2.088 x 1012 J / 5.60664 x 1010 J = 37

Therefore the published value is 37 times more than the calculated value

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