Estimations and Models Exercises

1 Unit Conversion J-BTU

There are 1055 joules in a BTU. If you have 20 BTU of energy, what is that quantity of energy when expressed in kilojoules?

2 Unit Conversion Gal-GJ

There are 115,000 BTU in a gallon of gasoline. How many gigajoules are in a 12-gallon tank of gas?

3 Mega to Giga

Express the quantity of 10,000 megajoules in gigajoules using our factor-label unit conversion method.

4 Prefixes

How many kilojoules are in a megajoule?

5 Power to Energy

You have a hair dryer that uses approximately 750 watts of power. If you use this hair dryer for 6 hours, how much energy does it use in kilowatt-hours?

6 Energy to Power

A phone battery can store approximately 22 kJ of electrical energy. What power in watts will charge the battery in 4 hours.

Electric Vehicle Fuel Costs

A local charging station charges at 6.6 kW of power and charges 1 USD per hour. Find the numbers for an electric vehicle and compute the electricity cost per mile.

Internal Combustion Fuel Costs

Assume gasoline costs 5 USD/gal.

Find the data for a vehicle and compute the fuel cost per mile.

Coal Energy Density

How much heat energy is released by burning 20 kg of coal?

Vehicle Charging

What power is needed to charge a 70 kWh battery in 15 minutes? Give your answer in kW.

Rate of EV and ICV Charging

What rate of electric charging is necessary to get equivalent miles per hour of energy loaded on to the vehicle?

Hint: set the miles per hour of charging for EV and ICV equal and solve for electric power

Vehicle Weights

A 70 kWh battery for an electric vehicle weighs about 500 kg. How much would a tank of gas with the same amount of energy weigh? Give your answer in kg.

  • What kind of quantity do you need for this?
  • Where can you find an estimate of the quantity?
  • Show your calculation.

Coal Energy Efficiency

Assume a coal plant is 37% efficient at transforming thermal energy into electrical energy. If you need 50 MWh of electricity, how many MWh of thermal energy from the coal do you need?

Coal Combustion

The EPA Reports that in 2019, the fossil fuel emissions in the US was 6577 million metric tons of carbon dioxide (equivalent). Recall that 12 kg of carbon produce 44 kg of carbon dioxide. How many kilograms of coal must be burned to generate this much carbon dioxide? You can assume that this coal is pure carbon.

Coal Plant Carbon Intensity

Carbon From Electricity Consumption

A customer switches from PG&E electricity at 238 grams CO2 per kWh to SCP Clean Start electricity at 58 grams CO2 per kWh.

If they use 10,000 kWh per year, what is the mass in metric tons of carbon dioxide emissions they avoid?

NOx Emissions

Assume a household uses 50 MMBTU (50 million BTU) of natural gas per year and they generate 0.034 kg NOx per MMBTU.

How many kilograms of NOx do they release?

Carbon Intensity of Electricity for Driving

What carbon intensity of electricity would make the per mile emissions of an EV equal to an ICV? Note that gasoline emits 8.89 kg of CO2 for every gallon burned. Assume of 40 mile per gallon vehicle and a 4 mile per kWh vehicle.

7 Power Plant Energy

A power plant produces 1.5 MW of power while running. If this plant runs continuously for one day, how much energy in joules (or gigajoules) does it produce?

8 World Power

The world uses approximately 500 exajoules per year. Express this as a power in watts.

9 Custom Energy Quantity

Come up with your own interesting energy quantity. It could be of any energy type. This exercise is to get you thinking about how to estimate the quantity, we are not interested in an accurate estimation yet.

  • Define your energy unit clearly with a physical description.
  • Define the input quantities clearly.
  • Optional: Express the quantity in units of joules.

10 MacKay Balance Sheet Reading

Please read this chapter from MacKay Sustainability Without All of the Hot Air. You can also find a link here. Then answer the following questions in complete sentences:

  • Can energy be created or destroyed?
  • How would you explain energy to a non-expert?
  • How would you explain power?

11 Personal Gasoline Model Outline

In your notes or on a piece of paper, write the components simple energy model (on a single page) to predict your annual automobile gasoline consumption. If you are comfortable, try to make an estimate. If not, clearly articulate what you know and don’t about making an estimate. Take a photo of this model and submit it as your assignment.

12 Personal Gasoline Model Estimate

Revisit your personal gasoline model from the last class period. Now, using your knowledge of energy quantities and units, make a quantitative estimate of your gasoline use in a year.

Write this out on paper with enough clarity that someone could understand your model. Then take a photo and upload to Canvas.

13 GEP 280 and ER 100 Readings

Please read the following two links and answer these questions in complete sentences.

14 H&K Chapter 2 Energy Mechanics

As you go through the reading, focus on the concepts. You will not be expected to reproduce all the calculations in this chapter. You also don’t need to read the appendix on Newton’s Laws of Motion.

Here is a link to the reading

  • Give an example of a simple energy conversion you find interesting and explain what type of input energy is converted into what type of output energy
  • Give an example of an energy conversion that has more than one step and explain each of the energy steps.

Supertanker

A supertanker as a ship that can carry 2 million barrels of oil to anywhere in the world.

  • How much chemical energy is this in Joules?
  • What do you think we should do to prevent this oil from spilling into the ocean?

Multiple Choice

  • A kilowatt-hour (kWh) is a unit of
    • energy
    • power
    • none of these
  • A kilowatt (kW) is a unit of
    • energy
    • power
    • none of these
  • Which of these would be best described by its power
    • car engine
    • car gasoline tank
    • neither
  • Which of these would be best described by its energy
    • car engine
    • car gasoline tank
    • neither
  • There are 3.6 megajoules in a kilowatt hour and 1055 joules in a BTU. Use these two facts to determine approximately how many btu are in 55 kWh.
    • 200 BTU
    • 200 thousand BTU
    • 200 million BTU
    • 200 billion BTU
  • A barrel of oil equivalent is the energy released by burning 42 gallons of crude oil. This is approximately $5.8 ^6 BTU. There are 1055 joules in a BTU. How many joules are in 10 barrels of oil equivalent?
    • 61 Billion joules
    • 55 Thousand joules
    • 61 Million joules
    • 6.1 Billion joules

Coal Plant

Assume a coal plant consumes 1.2 GJ of coal and produces 500 MJ of electrical energy.

  • What is the energy efficiency of this plant?
  • Does the energy efficiency in question 1 have units? Does it have dimensions?
  • How much carbon dioxide in pounds is released when a coal plant burns 2.0 GJ of coal? You can assume the coal is “bituminous”.

Boiling Energy Density

Assume it takes about 2 MJ of energy to boil a large pot of water. Assume coal has an energy density of 20 MJ per kg. Assume gasoline has an energy density of 45 MJ per kg.

  • How many kilograms of coal do you need to provide this energy?
  • How many kilograms of gasoline do you need?
  • How would you determine the volume of coal or gasoline you need?

Prefixes

  • Write the quantity 1 EJ (exajoule) using scientific notation and joules. (For example 1 kJ = 103 J.)
  • Write the quantity 1 MJ (megajoule) using scientific notation and joules.
  • Clearly show how to find the number of kilojoules in one megajoule. (Your answer should include scientific notation.)
  • Clearly show how to find the number of megajoules in one exajoule.

SSU Estimations

SSU electricity use per year is approximately 20 million kWh. Assuming a carbon intensity of electricity of 0.524 lbs CO2 per kWh, how many metric tons of carbon dioxide are emitted?

For the same electricity use and a carbon tax of $10 per metric ton of CO2, what would our carbon tax be for electricity?

Approximately 7000 parking permits are sold each year. We assume that each person drives to campus an average of 10 miles round trip four days a week in a car that gets 25 miles to the gallon. Assume these trips all occur during the 34 weeks of our semesters during the year. How much CO2 is emitted?

Suggest a policy or change to lower our transportation emissions and describe a method to estimate the reduction. By what percentage do you think this could lower transportation emissions? (You don’t have to do a complex estimate, just make a very crude estimate.)