Understanding Otto Cycle: Calculating Cycles, Heat Input, and Efficiency

[kris24tf]

Otto Cycle?? Please help ASAP!

I have a question that my entire class is confused over. I need help on it for a test, but I have no idea where to go with it. It doesn't seem to fit any of the equations or situations I have been using.

The question is: A four-stroke engine runs on the otto cycle. It delivers 150 hp at 3600 rpm. a) how many cycles are there in one minute?
I know that this is just 3600/2 = 1800 cycles

b) If the thermal efficiency of the engine is 20% what is the heat input per minute?

I don't know how to get this one. I know the equation I want is E=W/Q, but I don't know how to find the work done. do I use the 150 hp, 3600 rpm, or combine them somehow?

c)How much heat is wasted to the environment / minute.

I need the answer to part b I think for this right?

Any help at all would be great. Thanks for looking.

 

[mezarashi]

For (b), the 150 horse power is the clue.

1 hp = 0.7457 kW

What is the energy delivered in 1 minute.

 

[quicknote]

I would recommend approaching this problem by first understanding the concept of the Otto Cycle. The Otto Cycle is a thermodynamic cycle that describes the process of a four-stroke internal combustion engine, used in most cars and motorcycles. It consists of four stages: intake, compression, power, and exhaust. During the intake stage, the fuel-air mixture is drawn into the cylinder. In the compression stage, the mixture is compressed by the piston, increasing its temperature and pressure. In the power stage, the spark plug ignites the compressed mixture, causing an explosion and pushing the piston down, creating work. Finally, in the exhaust stage, the leftover gases are expelled from the cylinder.

Now, to answer the questions:

a) The engine runs at 3600 rpm, which means it completes 3600 revolutions in one minute. Since the Otto Cycle has two revolutions (up and down) per cycle, the number of cycles in one minute would be half of the revolutions, which is 1800 cycles.

b) To calculate the heat input, we need to use the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred. In this case, the heat input (Q) is equal to the work done (W) plus the heat wasted to the environment (Q_waste). So, the equation would be Q = W + Q_waste. To find the work done, we need to use the power output (150 hp) and the number of cycles per minute (1800). So, W = power output x number of cycles per minute = 150 hp x 1800 cycles/min = 270,000 hp-cycles/min. Now, we can use the efficiency (20%) to calculate the heat input: Q = W/efficiency = 270,000 hp-cycles/min / 0.20 = 1,350,000 hp-cycles/min.

c) To find the heat wasted to the environment, we can use the equation Q_waste = Q - W = 1,350,000 hp-cycles/min - 270,000 hp-cycles/min = 1,080,000 hp-cycles/min. This means that 1,080,000 hp-cycles of energy are wasted to the environment every minute.