Question

The efficiency of an engine is \(0.21 .\) For every \(1.00 \mathrm{kJ}\) of heat absorbed by the engine, how much (a) net work is done by it and (b) heat is released by it?

Short answer

Answer: The net work done by the engine is 0.21 kJ, and the heat released is 0.79 kJ.

Step-by-step solution

Recall the formula for efficiency

In thermodynamics, the efficiency of an engine can be calculated using the formula: $$Efficiency = \frac{Work\, output}{Heat\, absorbed}$$

Calculate the net work output

In this case, we are given the efficiency of the engine (0.21) and the amount of heat absorbed (1.00 kJ). We can rearrange the efficiency equation to find the work output: $$Work\, output = Efficiency × Heat\, absorbed$$ By plugging in the given values, we get: $$ Work\, output = 0.21 × 1.00 \, kJ = 0.21\, kJ $$

Calculate the heat released

The relationship between heat absorbed, work output, and heat released can be expressed as: $$Heat\, absorbed = Work\, output + Heat\, released$$ Now, we can rearrange the equation to solve for the heat released, which will look like: $$Heat\, released = Heat\, absorbed - Work\, output$$ Plugging in the values we have already found: $$ Heat\, released = 1.00\, kJ - 0.21\, kJ = 0.79\, kJ $$

Results

(a) The net work done by the engine is 0.21 kJ. (b) The heat released by the engine is 0.79 kJ.