The engine of a large ship does 2.05 multiplied by 108 J of work with an efficiency of 4.00%.
(a) How much waste heat (J) is produced?
(b) How many barrels of fuel are consumed, if each barrel produces 6.00 multiplied by 109 J of heat when burned?
W=2.05•10⁸ J
η= 4.00%=> η = 0,04
Q =W/0.04=5.125•10⁹ J
Waste heat = Q - W = 5.125•10⁹-2.05•10⁸ = 4.92•10⁹ J
N= 5.125•10⁹/6•10⁹ = 0.85
What are the dimensions of the 2.05? Meters displacement?
To answer your questions, we need to use the concept of efficiency to determine the amount of useful work done and the waste heat produced.
(a) To calculate the waste heat produced, we first need to find the amount of useful work done. The efficiency of the engine is given as 4.00%, which can be expressed as 0.040 (4.00/100). The formula for efficiency is:
Efficiency = Useful work output / Total energy input
Since we know the efficiency and the total work done, we can rearrange the equation to find the useful work output:
Useful work output = Efficiency * Total energy input
Useful work output = 0.040 * 2.05 * 10^8 J
Now, to find the waste heat, we can subtract the useful work output from the total energy input:
Waste heat = Total energy input - Useful work output
Waste heat = 2.05 * 10^8 J - (0.040 * 2.05 * 10^8 J)
Calculating the above expression, we get:
Waste heat = (1 - 0.040) * 2.05 * 10^8 J
Waste heat = 0.96 * 2.05 * 10^8 J
Waste heat = 1.968 * 10^8 J
Therefore, the waste heat produced is 1.968 x 10^8 J.
(b) To determine the number of barrels of fuel consumed, we need to find the total energy input. From the information provided, each barrel of fuel produces 6.00 * 10^9 J of heat when burned.
We can calculate the total energy input by dividing the total work done by the efficiency:
Total energy input = Total work done / Efficiency
Total energy input = 2.05 * 10^8 J / 0.040
Total energy input = 5.125 * 10^9 J
Now, we can find the number of barrels of fuel consumed by dividing the total energy input by the energy produced by each barrel:
Number of barrels of fuel consumed = Total energy input / Heat produced by each barrel
Number of barrels of fuel consumed = 5.125 * 10^9 J / (6.00 * 10^9 J)
Calculating the above expression, we get:
Number of barrels of fuel consumed = 0.8541667
Therefore, the number of barrels of fuel consumed is approximately 0.854 barrels.
To solve this problem, we need to understand the concept of efficiency and how it relates to the amount of work done and the waste heat produced.
(a) To determine the waste heat produced by the engine, we need to know that efficiency is defined as the ratio of useful work done by an engine to the total energy input. In this case, the efficiency is given as 4.00%. The efficiency can be calculated using the formula:
Efficiency = (Useful work output / Total energy input) * 100
Since the efficiency is given as 4.00% (or 0.04 as a decimal), we can rearrange the formula to find the useful work output:
Useful work output = Efficiency * Total energy input
In this case, the total energy input is given as 2.05 multiplied by 10^8 J. Let's plug in the values:
Useful work output = 0.04 * (2.05 multiplied by 10^8 J)
Now calculate the useful work output.
(b) To find the number of barrels of fuel consumed, we need to know the amount of heat produced by each barrel of fuel when burned. In this case, it is given that each barrel produces 6.00 multiplied by 10^9 J of heat.
To calculate the number of barrels of fuel consumed, we divide the total energy input by the energy produced by each barrel. Let's set up and solve the equation:
Number of barrels = Total energy input / Energy produced by each barrel
In this case, the total energy input is the same as the useful work output calculated in part (a).
Number of barrels = Useful work output / Energy produced by each barrel
Now calculate the number of barrels of fuel consumed.
Remember to perform the necessary calculations using the given values and the formulas provided to find the waste heat produced and the number of barrels of fuel consumed.