A gas within a piston-cylinder assembly executes a Carnot power cycle during which the isothermal expansion occurs at TH = 1500 K and the isothermal compression occurs at TC = 290 K. Determine: (a) the thermal efficiency. (b) the percent change in thermal efficiency if TH increases by 5% while TC remains the same. (c) the percent change in thermal efficiency if TC decreases by 5% while TH remains the same. (d) the percent change in thermal efficiency if TH increases by 5% and TC decreases by 5%.

a) 80.67%

b) 1.14%

c) 1.19%

d) 0.05%

Explanation:

The maximum efficiency in a heat engine is expressed as;

1-Tc/Th

where Tc=temperature of the cold 'sink

Th=temperature of the heat reservoir

Given that Tc=290 K and Th = 1500 K then;

a) thermal efficiency = 1 - 290/1500 = 0.8067 = 80.67%

b) Increasing TH by 5% will be 105/100 * 1500 = 1575 K

New thermal efficiency = 1 - 290/1575 = 0.8159 = 81.59%

Change in thermal efficiency = 0.8159-0.8067 = 0.0092

Percentage change in thermal efficiency = change in thermal efficiency/initial thermal efficiency * 100

0.0092 / 0.8067 * 100 = 1.14%

c) Decrease TC by 5% = 95/100 * 290 = 275.5 K

New thermal efficiency = 1-275.5/1500 = 0.8163 = 81.63%

change in thermal efficiency = 0. 8163-0.8067 = 0.0096

percent change in thermal efficiency = 0.0096/0.8067 * 100 = 1.19%

d) If TH is increased by 5%, thermal efficiency is 0.8159 as in (b) above

if TC is decreased by 5%, thermal efficiency is 0.8163 as in (c) above

The change in thermal efficiency = 0.8163-0.8159 = 0.0004

percent change in thermal efficiency = 0.0004/0.8067 * 100 = 0.05%