Question

An inventor claims to have developed a power cycle operating between hot and cold reservoirs at 1350 K and 295 K, respectively, that provides a steady-state power output of (a) 30.00 kW, (b) 33.33 kW, while receiving energy by heat transfer from the hot reservoir at the rate 150,000 kJ/h. Evaluate each claim.

Answer 1

Answer:

efficiency = 0.71999  <    0.78148  

efficiency = 0.7999   ≈     0.78148  

Explanation:

given data

Hot reservoir Temp Th = 1350 K

Cold reservoir Temp Tc = 295 K

heat transfer rate  = 150,000 kJ/h

solution

first we get here maximum possible efficiency that is express as

maximum possible efficiency = 1 -  $\frac{Tc}{Th}$   ..........1

put here value  and we get

maximum possible efficiency = 1 - $\frac{295}{1350}$

maximum possible efficiency = 0.78148  

and

efficiency = $\frac{Wout}{Qin}$   .................2

here Qin = $\frac{150000}{3600}$  = 41.667

so put here value in equation 2 we get

efficiency = $\frac{30}{41.667}$  

efficiency = 0.71999  <    0.78148  

and

efficiency = $\frac{33.33}{41.667}$  

efficiency = 0.7999   ≈     0.78148  

claim might be true or not because there always be looser