a. The quantity of heat rejected by the Carnot engine is equal to -101.2 kJ/s.
b. The power developed by the Carnot engine is equal to 148.8 kJ/s.
Given the following data:
- Quantity of heat received = 250 kJ/s
- Temperature of heat-source = 525°C
- Temperature of heat rejected = 50°C
Conversion:
Temperature of heat-source = 525°C to Kelvin = 525 + 273 = 798K
Temperature of heat rejected = 50°C to Kelvin = 50 + 273 = 323K
To find the power developed and the heat rejected, we would use Carnot's equation:
[tex]-\frac{Q_R}{T_R} = \frac{Q_S}{T_S}[/tex]
Where:
- [tex]Q_R[/tex] is the quantity of heat rejected.
- [tex]T_R[/tex] is the heat-sink temperature.
- [tex]T_S[/tex] is the heat-source temperature.
- [tex]Q_S[/tex] is the quantity of heat received.
Making [tex]Q_R[/tex] the subject of formula, we have:
[tex]Q_R = -( \frac{Q_S}{T_S})T_R[/tex]
Substituting the given parameters into the formula, we have;
[tex]Q_R = -( \frac{250}{798}) \times 323\\\\Q_R = -( \frac{80750}{798})[/tex]
Quantity of heat rejected = -101.2 kJ/s
Now, we can determine the power developed by the Carnot engine:
[tex]P = -Q_S - Q_R\\\\P = -250 - (-101.2)\\\\P = -250 + 101.2[/tex]
Power, P = 148.8 kJ/s.
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