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Rather than using a traditional solar chip, each dish focuses sunlight onto a 75

ID: 1699382 • Letter: R

Question

Rather than using a traditional solar chip, each dish focuses sunlight onto a 750kg engine of metal pistons filled with hydrogen. The gas heats to 720°C and expands the piston,
driving a generator to produce electricity. You may assume the hydrogen gas is part of a Carnot cycle and has Cp = 3/2 nR. As the gas cools, the piston returns to its original position. The efficiency of the process is quoted as 30%. 20,000 dishes produce 500 megawatts of work.
iii) What is the temperature of the cool gas?
iv) What is the heat per second expelled into the environment from the piston of only one dish?
v) What is the change of entropy over one round trip of the piston of only one dish as the hydrogen heats and cools?

Explanation / Answer

T1 = 720 0c

= 0.3

Q1(due to 20000 dishes) = 500 * 10^6 Watt

iii) Let temparature of cool gas = T2

We have, = 1 - (T2/T1)

T2 = (1-)T1 = 5040c

iv) Heat produced due to one dish, Q1 =  (500 * 10^6)/2 * 10^4 = 2.5 * 10^4 Watt

We have, = 1 - (Q2/Q1)

Q2 = (1-)Q1 = 1.75 * 10^4 Watt

v)Initial entropy, 1 = Q1/T1 = 0.69 * 10^6 Watt/0c

final entropy, 2 = Q2/T2 = 34.7 Watt/0c

Change in entropy = 1 - 2 = 6.9 * 10^5 Watt/0c