An engine receives 780 J of heat from a hot reservoir and does 180 J of work. What is the efficiency of this engine? What is the heat given off to the cold reservoir?
To find the efficiency of an engine, we need to use the formula:
Efficiency = (Work output / Heat input) * 100%
In this case, the work output is given as 180 J and the heat input is given as 780 J. Plugging these values into the formula, we get:
Efficiency = (180 J / 780 J) * 100%
Simplifying the expression, we have:
Efficiency = 0.2307 * 100%
Efficiency ≈ 23.07%
So, the efficiency of this engine is approximately 23.07%.
To find the heat given off to the cold reservoir, we can use the principle of energy conservation. The heat given off to the cold reservoir (Qc) is equal to the difference between the heat input (Qh) and the work output (W):
Qc = Qh - W
Plugging in the given values, we have:
Qc = 780 J - 180 J
Qc = 600 J
Therefore, the heat given off to the cold reservoir is 600 J.