To determine the thermal efficiency of the engine, we can use the formula:
Thermal Efficiency = Work output / Heat input
Let's calculate each of these values step by step:
1. Work Output:
The work output of the engine can be calculated using the torque and engine speed. The formula for work is:
Work = Torque x Distance x Revolutions
In this case, the torque is 200 N, the distance is 1 meter, and the engine speed is 1500 r/min. So, the work output is:
Work = 200 N x 1 m x 1500 r/min = 300,000 Nm/min
2. Heat Input:
The heat input is equal to the energy content of the gasoline consumed by the engine during the test. To calculate the heat input, we need to determine the energy content of the gasoline used.
The volume of gasoline used is 3-3/4 liters, which is equal to 3.75 liters.
The density of the gasoline is 0.70, so the mass of the gasoline used is:
Mass = Volume x Density = 3.75 liters x 0.70 kg/liter = 2.625 kg
The heating value of the gasoline is 44.432 MJ/kg, so the heat input is:
Heat Input = Mass x Heating Value = 2.625 kg x 44.432 MJ/kg = 116.519 MJ
Converting the heat input from MJ to J:
Heat Input = 116.519 MJ x 10^6 J/MJ = 116519000 J
Now, we can calculate the thermal efficiency using the formula:
Thermal Efficiency = Work output / Heat input = 300,000 Nm/min / 116519000 J
Simplifying the units:
1 Nm/min = 1 J/s
1 J/min = 1 J/s
So, Thermal Efficiency = 300,000 J/min / 116519000 J = 0.00257417
Rounding the value to four decimal places, the thermal efficiency of the engine is approximately 0.0026.
It is proposed to use a standard gasoline engine with a compression ratio of 6:1 for an industrial operation. A test is conducted to determine the efficiency of the engine. Gasoline with a density of 0.70 an a heating value of 44.432 MJ/kg is used for the test. A torque device measures 200 N at a distance of one meter at an engine speed of 1500 r/min. The engine uses 3-3/4 liters of gasoline in 15 min. while developing that torque. Which of the following most nearly equals the thermal efficiency of the engine?
1 answer
1 answer