A heat engine operating b/n 100°c and 700°c has an efficiency equal to 40% of the maximum theoretical efficiency. How much energy does this extract from the hot reservoir in order to do 5000J of machanical work?

answer

getachew

Student

20270

20,000

To solve this problem, we'll first need to know the maximum theoretical efficiency for a heat engine operating between two temperature reservoirs. The maximum theoretical efficiency can be calculated using the Carnot efficiency formula:

Carnot efficiency = 1 - (Tc/Th)

Where Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir.

In this case, the temperature of the cold reservoir (Tc) is given as 100°C and the temperature of the hot reservoir (Th) is given as 700°C.

Let's calculate the maximum theoretical efficiency:

Carnot efficiency = 1 - (Tc/Th)
= 1 - (100/700)
= 1 - 0.1429
= 0.8571

Now, we are given that the efficiency of the heat engine is 40% of the maximum theoretical efficiency. Thus, the efficiency of the heat engine is:

Efficiency = 0.4 * Carnot efficiency
= 0.4 * 0.8571
= 0.3429

Now, we can calculate the energy extracted from the hot reservoir to do 5000J of mechanical work. The formula to calculate the energy extracted is:

Energy extracted = (work done / Efficiency)

Substituting the given values:

Energy extracted = (5000 J / 0.3429)
≈ 14604 J

Therefore, the heat engine extracts approximately 14604 Joules of energy from the hot reservoir in order to do 5000 Joules of mechanical work.