A steam engine absorbs 1.98*10^5 J and expels 1.49*10^5 J in each cycle. Assume that all of the remaining energy is used to do work.
a. What is the engine's efficiency?
b. How much work is done in each cycle?
If a gasoline engine has an efficiency of 21 percent and loses 780 J to the cooling system and exhaust during each cycle, how much work is done by the engine?
Efficiency= useful work/inputwork * 100
.21 Input work= 780J
solve for input work
thenuseful work= .79*input work
the first one the answer for a is 25% and for b is 4.9 x 10^4 J.
To find the answers to these questions, we can use the formula for efficiency:
Efficiency = (Useful work / Input work) * 100
Let's start with the first question:
a. What is the engine's efficiency?
Given:
Input work = 1.98 * 10^5 J
Output work = 1.49 * 10^5 J
To find the efficiency, we need to calculate the useful work.
Useful work = Input work - Output work = (1.98 * 10^5 J) - (1.49 * 10^5 J) = 0.49 * 10^5 J
Now, we can substitute the values into the efficiency formula:
Efficiency = (Useful work / Input work) * 100
Efficiency = (0.49 * 10^5 J / 1.98 * 10^5 J) * 100
Simplify and calculate:
Efficiency = (0.49 / 1.98) * 100 ≈ 24.75%
Therefore, the steam engine has an efficiency of approximately 24.75%.
b. How much work is done in each cycle?
The work done in each cycle is the output work:
Work done = Output work = 1.49 * 10^5 J
Therefore, the work done in each cycle is 1.49 * 10^5 J.
Moving on to the second question:
If a gasoline engine has an efficiency of 21 percent and loses 780 J to the cooling system and exhaust during each cycle, we can find the work done by the engine.
Given:
Efficiency = 21%
Energy lost = 780 J
First, we need to calculate the input work.
Input work = Energy lost / Efficiency
Input work = 780 J / (21% / 100) = 780 J / 0.21
Calculate input work:
Input work = 780 J / 0.21 ≈ 3714.29 J
Next, we can find the useful work:
Useful work = Efficiency * Input work = 21% * 3714.29 J
Calculate the useful work:
Useful work = 0.21 * 3714.29 J ≈ 779.99 J
Therefore, the work done by the gasoline engine is approximately 779.99 J.
a. To find the engine's efficiency, we need to calculate the ratio of the useful work done by the engine to the input work (energy absorbed by the engine). The formula to calculate efficiency is:
Efficiency = (Useful work / Input work) * 100
Given that the steam engine absorbs 1.98 * 10^5 J and expels 1.49 * 10^5 J in each cycle, we can calculate the remaining energy used to do work:
Remaining energy = Energy absorbed - Energy expelled
Remaining energy = 1.98 * 10^5 J - 1.49 * 10^5 J
Remaining energy = 0.49 * 10^5 J
Remaining energy = 4.9 * 10^4 J
Therefore, the useful work done by the engine in each cycle is 4.9 * 10^4 J.
Now, we can calculate the engine's efficiency using the formula mentioned above:
Efficiency = (4.9 * 10^4 J / 1.98 * 10^5 J) * 100
Efficiency ≈ 24.74%
b. To calculate the work done in each cycle, we consider the remaining energy used to do work, which is 4.9 * 10^4 J. Therefore, the work done in each cycle by the engine is 4.9 * 10^4 J.
Now, let's move on to the second part of the question.
For the gasoline engine with an efficiency of 21 percent, we are given that it loses 780 J to the cooling system and exhaust during each cycle. This means that the useful work is only 79% of the input work.
To find the input work, we can rearrange the efficiency formula:
Efficiency = (Useful work / Input work) * 100
21 = (79 / Input work) * 100
Now, we can solve for the input work:
Input work = 79 / (21 / 100)
Input work = 79 * 100 / 21
Input work ≈ 376 J
Using the formula for useful work mentioned in the question, we can calculate the work done by the engine:
Useful work = 0.79 * Input work
Useful work = 0.79 * 376 J
Useful work ≈ 296.04 J
Therefore, the work done by the gasoline engine in each cycle is approximately 296.04 J.