Energy Calculation - Car, Diesel & Battery Power

[boyblair]

Hi everyone!

I am having a bit of a problem solving the following question (not good with maths), and would be very grateful for any advice given.

Homework Statement

A car is run for 400 hours per year, with a total mileage of 10,000 a year. The car uses diesel and consumes 2,000 litres per year. A litre of diesel cost £1.10 and holds 38.7MJ of primary energy.

a) Calculate the mean engine power?

b) If the engine is 20% efficient overall, how much energy would need to be stored in 95% efficient batteries to give a range of 300 miles on full battery charge?

Many thanks,

 

[djeitnstine]

you say you're not good at math but that doesn't tell us where you need help at.

Where is your attempt?

 

[Mene]

I would approach this problem by first understanding the basic principles of energy and power. Energy is the ability to do work, while power is the rate at which energy is used or transferred. In the context of a car, power is the rate at which the car's engine can convert fuel into motion.

With this in mind, let's tackle the first part of the question: calculating the mean engine power. To do this, we need to use the formula P = E/t, where P is power in watts, E is energy in joules, and t is time in seconds. We are given the total energy consumption of the car (2,000 litres of diesel, each with 38.7MJ of energy) and the total time the car is in operation (400 hours). We can convert the energy from litres to joules by multiplying by the conversion factor of 38.7MJ/L. Plugging these values into the formula, we get P = (2,000 x 38.7MJ) / (400 hours x 3600 seconds/hour) = 214.5 watts. This is the mean engine power of the car.

Moving on to the second part of the question, we need to consider the efficiency of the car's engine and the batteries. The engine is said to be 20% efficient, meaning that only 20% of the energy from the fuel is actually used to power the car. The remaining 80% is lost as heat and other forms of energy. On the other hand, the batteries are said to be 95% efficient, meaning that 95% of the energy stored in them can be used to power the car.

To calculate the amount of energy needed to power the car for a range of 300 miles, we can use the formula E = P x t, where E is energy in joules, P is power in watts, and t is time in seconds. We know that the car's engine has a power of 214.5 watts, and we want to travel 300 miles (480,000 meters) in that time. Using the distance formula, we can calculate the time it would take to travel 300 miles at a speed of 60 miles per hour (26.8 m/s), which is approximately 17,910 seconds. Plugging these values into the formula, we get E = 214.5 watts x 17,910 seconds =