Question

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%.

Answer 1

a) 80.67%

b)1.14%

c)1.19%

d)0.05%

Step-by-step 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%