A person performs a work task at a mechanical efficiency of 20 percent and at total energy output of 15kcal/min. How much energy(kcal/min) is lost as heat? and how much energy(kcal/min) is used to actually perform the work?
To find the amount of energy lost as heat and the amount of energy used to perform the work, we can use the concept of mechanical efficiency.
Mechanical efficiency is defined as the ratio of work output to the total energy input. In this case, the mechanical efficiency is given as 20 percent, which can be written as 0.20.
Total energy input (E) = Energy used to perform the work (W) + Energy lost as heat (Q)
Since mechanical efficiency is the ratio of work output to total energy input, we can write:
W/E = 0.20
Given that the total energy output is 15 kcal/min, we can substitute the values:
W/15 = 0.20
Now, let's solve for the energy used to perform the work:
W = 0.20 * 15
W = 3 kcal/min
Therefore, the energy used to perform the work is 3 kcal/min.
To find the energy lost as heat, we can subtract the energy used to perform the work from the total energy output:
Q = 15 - 3
Q = 12 kcal/min
Therefore, the energy lost as heat is 12 kcal/min.
To find out the amount of energy lost as heat and the amount of energy used to perform the work, we first need to calculate the total energy input.
The mechanical efficiency is given as 20%, which means only 20% of the total energy input is converted into useful work. Therefore, the remaining 80% is lost as heat.
Step 1: Calculate the total energy input.
Total energy input = Total energy output / Mechanical efficiency
Given that the total energy output is 15 kcal/min and the mechanical efficiency is 20% (or 0.2), we can calculate the total energy input as follows:
Total energy input = 15 kcal/min / 0.2 = 75 kcal/min
Step 2: Calculate the energy lost as heat.
Energy lost as heat = Total energy input - Energy used for work
Energy used for work = Total energy output
Substituting the values, we have:
Energy lost as heat = 75 kcal/min - 15 kcal/min = 60 kcal/min
Therefore, 60 kcal/min is lost as heat.
Step 3: Calculate the energy used to perform the work.
Energy used to perform the work = Total energy output
From the information given, it is stated that the energy used to perform the work is 15 kcal/min.
Therefore, 15 kcal/min is used to actually perform the work.