Question

A heat engine receives heat from a source at 1000∘C and rejects the waste heat to a sink at 50∘C. If heat is supplied to this engine at a rate of 100 kJ/s, the maximum power this heat engine can produce is (a) 25.4 kW (b) 55.4 kW (c) 74.6 kW (d) 95.0 kW (e) 100 kW

Answer 1

Answer:

D. 95.0kW

Explanation:

Temperature of heat supplied = 1000°C

Temperature of waste heat = 50°C

Temperature of maximum power produced = 1000°C - 50°C = 950°C

Rate of heat supplied = 100kJ/s = 100kW

Maximum power produced = 950°C/1000°C × 100kW = 95kW

Answer 2

The maximum power this heat engine can produce is 74.6 kW.

What is a heat engine?

In the engineering field, heat energy helps to convert heat energy to mechanical energy.

From the parameters given:

• Temperature from the source $\mathbf{T_H = 1000^0 C}$ = 1273 K
• The temperature in the sink $\mathbf{T_L = 50 ^0 C}$ = 323 K
• The heat supplied to the engine $\mathbf{Q_H = 100 \ kJ/s}$

From the above information, we can determine the maximum possible efficiency for the heat engine by using the Carnot efficiency.

$\mathbf{\eta_{rev}= 1 -\dfrac{T_L}{T_H} }$

$\mathbf{\eta_{rev}= 1 -\dfrac{323}{1273} }$

$\mathbf{\eta_{rev}= 0.746 }$

From the efficiency formula, we can determine the maximum power of the heat engine.

i.e.

$\mathbf{\eta_{rev} = \dfrac{W_{in}}{Q_H}}$

$\mathbf{ W_{in} =\eta_{rev} \times {Q_H}}$

$\mathbf{ W_{in} =0.746 \times(100) \ kJ/s}$

$\mathbf{ W_{in} =74.6 \ kJ/s}$

$\mathbf{ W_{in} =74.6 \ kW}$

Therefore, we can conclude that the maximum power this heat engine can produce is 74.6 kW.

Learn more about heat engines here:

https://brainly.com/question/24707911