A certain heat engine does 8.0 kJ of work and dissipates 8.00 kJ of waste heat in a cyclical process.
(a) What was the heat input to this engine?
(b) What was its efficiency?
Heat input Q=W+Q₁ =
=8000+8000 = 16000 J
η=W/Q =8000/16000=0.5
η =50%
To determine the heat input to the engine, we need to apply the First Law of Thermodynamics, which states that the heat input is equal to the work done by the engine plus the waste heat dissipated.
(a) Heat input:
Given:
Work done (W) = 8.0 kJ
Waste heat dissipated (Qwaste) = 8.00 kJ
Using the First Law of Thermodynamics:
Heat input (Qin) = Work done (W) + Waste heat dissipated (Qwaste)
Qin = 8.0 kJ + 8.00 kJ
Qin = 16.0 kJ
Therefore, the heat input to the engine is 16.0 kJ.
(b) Efficiency:
The efficiency of a heat engine is given by the ratio of the work done by the engine to the heat input.
Efficiency = (Work done / Heat input) * 100%
Given:
Work done (W) = 8.0 kJ
Heat input (Qin) = 16.0 kJ
Efficiency = (8.0 kJ / 16.0 kJ) * 100%
Efficiency = 0.5 * 100%
Efficiency = 50%
Therefore, the efficiency of the heat engine is 50%.
To find the heat input to the engine, we can use the first law of thermodynamics, which states that the total energy change in a system is equal to the heat input minus the work done by the system. Mathematically, this can be represented as:
ΔE = Q - W
Where:
ΔE is the change in energy of the system
Q is the heat input
W is the work done by the system
In this case, we are given that the engine does 8.0 kJ of work, so we can substitute this value into the equation:
8.0 kJ = Q - 8.0 kJ
To find Q, we can rearrange the equation:
Q = 8.0 kJ + 8.0 kJ
Q = 16.0 kJ
So, the heat input to the engine is 16.0 kJ.
To find the efficiency of the heat engine, we can use the efficiency formula for heat engines:
Efficiency = (Work output / Heat input) x 100%
Since the work output is the same as the work done by the system, which is given as 8.0 kJ, and the heat input is 16.0 kJ, we can substitute these values into the formula:
Efficiency = (8.0 kJ / 16.0 kJ) x 100%
Efficiency = 0.5 x 100%
Efficiency = 50%
So, the efficiency of the heat engine is 50%.