Math Problem Statement

Find the efficiency as a percentage for the following cases: 1. A power generation station with input power 450,000 MW and output power 95,000 MW. 2. A four-stroke diesel engine with input power 80 kW (from fuel) and output power 22 kW (brake power).

Solution

The problem is asking for the efficiency of two different engines. The efficiency is defined as:

Efficiency(%)=(Output PowerInput Power)×100\text{Efficiency} (\%) = \left( \frac{\text{Output Power}}{\text{Input Power}} \right) \times 100

Let's break it down:

a) Power generation station:

  • Input power = 450,000 MW
  • Output power = 95,000 MW

Using the formula:

Efficiency=(95,000450,000)×100\text{Efficiency} = \left( \frac{95,000}{450,000} \right) \times 100

b) Four-stroke diesel engine:

  • Input power = 80 kW
  • Output power = 22 kW

Using the formula:

Efficiency=(2280)×100\text{Efficiency} = \left( \frac{22}{80} \right) \times 100

I'll now calculate both efficiencies.The efficiencies for the two cases are:

a) Power generation station: 21.11%21.11\%
b) Four-stroke diesel engine: 27.50%27.50\%

Would you like further details or have any questions?

Here are five related questions to further explore:

  1. What factors influence the efficiency of power generation stations?
  2. How does the efficiency of diesel engines vary with load?
  3. What are common methods to improve engine efficiency?
  4. What is the typical efficiency range for power plants using different fuel types?
  5. How is energy lost in less efficient engines?

Tip: Engine maintenance and operating conditions greatly affect efficiency, making regular

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Math Problem Analysis

Mathematical Concepts

Efficiency
Percentage
Ratio

Formulas

Efficiency (%) = (Output Power / Input Power) * 100

Theorems

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Suitable Grade Level

Grades 9-12