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Water flowing steadily at 2 kg/s executes the Carnot power cycle shown. The cycl

ID: 1863231 • Letter: W

Question

Water flowing steadily at 2 kg/s executes the Carnot power cycle shown. The cycle produces a net power of 1.43 MW. Isothermal expansion occurs at a pressure of 800 kPa and changes the working fluid from a saturated liquid to a saturated vapor.


a. Determine the rate of heat transfer between the surroundings and the boiler (ans: ?12 = 4095 kW).

b. Determine the thermal efficiency (ans: 0.349).

c. At what temperature does the isothermal compression occur

(in

Water flowing steadily at 2 kg/s executes the Carnot power cycle shown. The cycle produces a net power of 1.43 MW. Isothermal expansion occurs at a pressure of 800 kPa and changes the working fluid from a saturated liquid to a saturated vapor. a. Determine the rate of heat transfer between the surroundings and the boiler (ans: ?12 = 4095 kW). b. Determine the thermal efficiency (ans: 0.349). c. At what temperature does the isothermal compression occur (in degreeC)? (ans: Tc = 15.7degreeC) d. Sketch the cycle on a p-v diagram with respect to the location of the vapor dome.

Explanation / Answer

given rate of mass = m' = 2kg/s

Isothermal expansion is from 1---> 2

state 1: saturated liquid at 800kPa => T1=Tsat = 170.43 C = 443.43 K

h1= hf = 721.10 kJ/kg

state 2: saturated vapor at 800kPa => T2=T1=443.43K

h2 = hg = 2769.13 kJ/kg

process 1--->2:

1st Law:   Q'(1 to 2) + m'h1 = m'h2 + W'(1 to 2)

as the work done in a boiler is zero. Q'(1 to 2)= m'(h2-h1)

= 2(2769.13-721.10)

= 4096.06 kW

= 4.0961 MW

Part a) Rate of heat transfer between surroundings and boiler = Q'(1 to 2) = 4.0961MW

Part b) Efficiency = W'net/Q'(1 to 2) = 1.43/4.0961 = 0.349

Part c) Efficiency can also be calculated by e= 1-(Tc/Th)=0.349

where Th is expansion temp. and Tc is compression temp.

=> Tc/Th = 0.651

=> Tc = 0.651 x 443.43 = 288.67 K = 15.67 C