A theoretical gasoline engine runs with 76 percent efficiency. It is calculated that it expels 3.25*10^4 J of heat.
a. Find the heat absorbed in one cycle.
b. Find the work output in one cycle.
To find the heat absorbed in one cycle, we need to use the concept of efficiency.
a. The efficiency of the engine is given as 76 percent, or 0.76 in decimal form. Efficiency is defined as the ratio of the useful work output to the total heat input.
Given that the engine expels 3.25*10^4 J of heat, we can say that the useful work output is 0.76 times the total heat input. Thus, we can set up the following equation:
0.76 * Total heat input = 3.25*10^4 J
To find the total heat input, we divide both sides of the equation by 0.76:
Total heat input = (3.25*10^4 J) / 0.76
Plugging in the values into a calculator, the total heat input comes out to be approximately 42763.16 J.
Therefore, the heat absorbed in one cycle is approximately 42763.16 J.
b. The work output in one cycle can be calculated using the first law of thermodynamics, which states that the work done by the engine is equal to the heat absorbed minus the heat expelled.
Work output = Heat absorbed - Heat expelled
= 42763.16 J - 3.25*10^4 J
= 12080.84 J
Therefore, the work output in one cycle is 12080.84 J.