a carnot engine is designed to operate between 480K and 300K.if the engine actually produces 1.4j of mechanical energy per calorie of heat absorbed,then the ratio of actual efficiency to theoretical efficiency is
To find the ratio of actual efficiency to theoretical efficiency of a Carnot engine, we need to calculate both efficiencies separately.
1. Theoretical Efficiency:
The theoretical efficiency of a Carnot engine is given by the equation:
η_th = 1 - (T_cold / T_hot)
where T_cold is the temperature of the cold reservoir (300K) and T_hot is the temperature of the hot reservoir (480K).
η_th = 1 - (300 / 480)
= 1 - 0.625
= 0.375
2. Actual Efficiency:
The actual efficiency is calculated by dividing the mechanical energy produced per calorie of heat absorbed by the temperature difference between the hot and cold reservoirs:
η_actual = Mechanical Energy / (Heat Absorbed)
= 1.4J/cal / (T_hot - T_cold)
Here, T_hot is 480K and T_cold is 300K. Therefore,
η_actual = 1.4J/cal / (480 - 300)
= 1.4J/cal / 180
≈ 0.0078
Now, to find the ratio of actual efficiency to theoretical efficiency, we divide the actual efficiency by the theoretical efficiency:
Ratio = η_actual / η_th
= 0.0078 / 0.375
≈ 0.0208
So, the ratio of actual efficiency to theoretical efficiency is approximately 0.0208.