A steam turbine takes in 75g of water and boils it as heat energy to run a 40% efficient engine. How much work does this engine do per cycle?

• A. 67,800 J
• B. 1.695×10⁵ J
• C. 10,020 J
• D. 4.24×10⁵ J

Answer: (A)

Verified step by step guidance

1. First, understand that the problem involves converting heat energy into work using a steam turbine engine with a given efficiency. The efficiency of the engine is 40%, which means only 40% of the input energy is converted into work.
2. Calculate the heat energy required to boil 75g of water. Use the specific heat of vaporization for water, which is approximately 2260 J/g. Multiply this value by the mass of the water to find the total heat energy input: \( Q = 75 \text{ g} \times 2260 \text{ J/g} \).
3. Now, apply the efficiency formula to determine the work done by the engine. The efficiency \( \eta \) is given by \( \eta = \frac{W}{Q} \), where \( W \) is the work done and \( Q \) is the heat energy input. Rearrange this formula to solve for \( W \): \( W = \eta \times Q \).
4. Substitute the values into the efficiency formula: \( W = 0.40 \times Q \). Use the value of \( Q \) calculated in the previous step to find the work done.
5. Finally, compare the calculated work with the given options to determine which one matches the calculated value. This will help you identify the correct answer from the provided choices.