A Carnot engine working between 400oC and 40oC produces 130 kJ of work. Determine:
i. The engine thermal efficiency
ii. The heat added
To find the thermal efficiency of the Carnot engine, we can use the formula:
Efficiency = (1 - (Tc/Th)) * 100
Where:
Tc = temperature of the cold reservoir
Th = temperature of the hot reservoir
In this case, Tc = 40°C (273.15 + 40 = 313.15 K) and Th = 400°C (273.15 + 400 = 673.15 K).
Efficiency = (1 - (313.15/673.15)) * 100
Efficiency = (1 - 0.4646154) * 100
Efficiency ≈ 53.54%
Therefore, the engine has a thermal efficiency of approximately 53.54%.
To find the heat added to the engine, we can use the formula:
Efficiency = (Work output / Heat input) * 100
Given that the work output is 130 kJ, we can rearrange the formula to solve for heat input:
Heat input = (Work output / Efficiency) * 100
Heat input = (130 / 53.54) * 100
Heat input ≈ 242.72 kJ
Therefore, the heat added to the engine is approximately 242.72 kJ.
To determine the thermal efficiency and the heat added by a Carnot engine, we can use the formulas:
i. The Carnot efficiency (η) is given by the formula:
η = 1 - (Tc / Th)
ii. The work produced by the Carnot engine is given by:
W = Qh - Qc
Where:
η = thermal efficiency
Tc = temperature of the cold reservoir (in Kelvin)
Th = temperature of the hot reservoir (in Kelvin)
W = work produced by the engine (in Joules)
Qh = heat added to the engine (in Joules)
Qc = heat rejected by the engine (in Joules)
Given:
Tc = 40°C = 313.15 K (converted to Kelvin)
Th = 400°C = 673.15 K (converted to Kelvin)
W = 130 kJ = 130,000 J (converted to Joules)
Now, let's calculate the values:
i. The thermal efficiency (η):
η = 1 - (Tc / Th)
η = 1 - (313.15 / 673.15)
η ≈ 0.5357 or 53.57%
ii. The heat added (Qh):
W = Qh - Qc
130,000 J = Qh - Qc
Since the Carnot engine is reversible, the heat rejected (Qc) will be equal to the heat added (Qh) since the net heat transfer is zero.
Qh = Qc
Therefore,
Qh = Qc = 130,000 J
So, the heat added by the Carnot engine is 130,000 J.