Question

A well-insulated turbine operating at steady state develops 28.75 MW of power for a steam flow rate of 50 kg/s. The steam enters at 25 bar with a velocity of 61 m/s and exits as saturated vapor at 0.06 bar with a velocity of 130 m/s. Neglecting potential energy effects, determine the inlet temperature, in 8C.

Answer 1

The maximum theoretical efficiency for a heat engine operating between two temperatures can be determined using the Carnot efficiency formula. In this case, the maximum theoretical efficiency is 47.66%.

Step-by-step explanation:

The maximum theoretical efficiency for a heat engine operating between two temperatures can be determined using the Carnot efficiency formula:

Efficiency = 1 - Tc/Th

Where Tc is the absolute temperature of the cold reservoir and Th is the absolute temperature of the hot reservoir. In this case, the cold reservoir temperature is 27°C, which is 300K, and the hot reservoir temperature is 300°C, which is 573K. Plugging these values into the formula gives:

Efficiency = 1 - 300/573 = 0.4766

Therefore, the maximum theoretical efficiency for this heat engine is 47.66%.

Answer 2

Answer:
`355^(\circ)C`

Step-by-step explanation:

Given

power Developed=28.75 MW

`\dot{m}=50 kg/s`

`P_1=5 bar`

`v_1=61 m/s`

Steam exit as saturated

`P_2=0.06 bar`

`v_2=130 m/s`

From saturated steam stable h2=h_g=2567.4 KJ/kg[/tex]

Applying Steady flow Energy equation

`\dot{m}\left [ h_1+(1)/(2)\left ( v_1^2\right )+gz_1\right ]+Q=\dot{m}\left [ h_2+(1)/(2)\left ( v_2^2\right )+gz_2\right ]+W`

Q=0 because of insulation and

`z_1=z_2`

`h_1=\frac{W}{\dot{m}}-(1)/(2)\left ( v_1^2-v_2^2\right )+h_2`

`h_1=frac{28.75* 10^3}{50}-(1)/(2)\left ( 61^2-130^2\right )* (1)/(1000)+2567.4`

`h_1=3149 kJ/kg`

`At P_1=25 bar h_1=3149 kJ/kg`

using steam tables

`T_1=355^(\circ)C`