# Part B: "150W Engine Efficiency - Heat Given off Per Cycle

• jennypear
So you know that Q_{in} = 150 J and \eta = 0.25. You can use this information to find W_{out} and from there, Q_{out}.In summary, the engine has an output of 150W and an efficiency of 25%. It works at 10 cycles/s. In each cycle, 15.0 J of work is done and 15 J of heat is given off.
jennypear
An engine with an output of 150W has an efficiency of 25%. It works at 10 cycles/s.

A. How much work is done in each cycle?
work=power(delta t) = 150 W * 1s = 150 J
work =15.0 J per cycle

**got part A correct

B. How much heat is given off in each cycle?
delta internal energy = delta work + delta heat
delta intergy = 0 bc its a complete cycle
delta heat = - delta work
delta heat = 15 J

**Part B isn't coming out...please guide in the correct direction if possible.

Realize that what you are calling "delta heat" equals $Q_{in} - Q_{out}$. What you need to find is $Q_{out}$. Also recall the definition of efficiency: $\eta = W_{out}/Q_{in}$.

In order to calculate the heat given off per cycle, we need to first determine the amount of work done in each cycle. As we established in part A, the work done in each cycle is 15 J.

Next, we need to use the efficiency equation (efficiency = work output/energy input) to find the energy input. We know that the engine has an efficiency of 25%, so we can set up the equation as:

0.25 = 15 J/Energy input

Solving for energy input, we get:

Energy input = 60 J

This means that 60 J of energy is being input into the engine in each cycle.

Now, we can use the first law of thermodynamics (delta internal energy = delta work + delta heat) to find the heat given off per cycle. Since the engine is operating at a steady state, the delta internal energy is 0. We also know that the work done in each cycle is 15 J.

Therefore, we can set up the equation as:

0 = 15 J + delta heat

Solving for delta heat, we get:

Delta heat = -15 J

This means that 15 J of heat is being given off in each cycle.

In summary, the engine with an output of 150W, operating at 10 cycles/s, has an efficiency of 25% and gives off 15 J of heat in each cycle.

## 1. What is the purpose of studying engine efficiency?

The purpose of studying engine efficiency is to understand how efficiently an engine converts fuel into useful work. This information can help improve the design and operation of engines, leading to increased performance and reduced energy consumption.

## 2. How is engine efficiency measured?

Engine efficiency is typically measured by calculating the ratio of useful work output to the total energy input. In the case of the 150W engine, this is the ratio of heat given off per cycle to the total amount of heat supplied to the engine.

## 3. What factors affect engine efficiency?

The efficiency of an engine can be affected by various factors, including the type of fuel used, the design and condition of the engine, and the operating conditions such as temperature and pressure. Additionally, factors such as friction and heat loss can also impact the overall efficiency of an engine.

## 4. How does engine efficiency impact the environment?

Engine efficiency has a direct impact on the environment as it determines the amount of fuel needed to produce a certain amount of work. Higher engine efficiency means less fuel is required, leading to reduced emissions and a smaller carbon footprint.

## 5. Can engine efficiency be improved?

Yes, engine efficiency can be improved through various means such as optimizing the design and operation of the engine, using higher quality fuels, and implementing technologies such as turbocharging and hybrid systems. Regular maintenance and proper usage can also help improve engine efficiency.

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