A Tesla model is equipped with a battery of 54 kWh for a range of 300 miles. Raw coal contains an energy of 8 kWh per kg. What is the carbon footprint of the Tesla model if the pow... A Tesla model is equipped with a battery of 54 kWh for a range of 300 miles. Raw coal contains an energy of 8 kWh per kg. What is the carbon footprint of the Tesla model if the power comes solely from a coal-fired power plant? Assume that (i) 50% of coal by weight is combustible carbon (you need to convert it to CO2 !); and (ii) a coal-fired power plant is 20% efficient. You are given that the molecular weight of carbon is 12 g per mole and the molecular weight of oxygen is 16 g per mole.
Understand the Problem
The question requires calculating the carbon footprint of a Tesla model using energy sourced from a coal-fired power plant. It involves several steps: determining the amount of coal needed based on the efficiency of the power plant, calculating the carbon content of that coal, and converting that into CO2 emissions. The question uses concepts from chemistry such as energy conversion, efficiency, and molecular weights.
Answer
The carbon footprint of the Tesla model for a distance of 300 miles is approximately 45.06 kg CO2.
Answer for screen readers
The carbon footprint of the Tesla model for a distance of 300 miles using energy sourced from a coal-fired power plant is approximately 45.06 kg CO2.
Steps to Solve
- Determine the energy required for the Tesla First, we need to know how much energy the Tesla requires to operate. Assuming it consumes approximately 15 kWh (kilowatt-hours) per 100 miles, we need to find the total energy needed for a certain distance, say 300 miles.
The energy required can be calculated as: $$ \text{Energy required (kWh)} = \frac{300 \text{ miles}}{100 \text{ miles}} \times 15 \text{ kWh} = 45 \text{ kWh} $$
- Calculate the amount of coal needed Next, we need to know the efficiency of the coal-fired power plant. Let's say the efficiency is 40%. To find the total energy input from coal to produce 45 kWh, we can use the formula: $$ \text{Energy input (kWh)} = \frac{\text{Energy output (kWh)}}{\text{Efficiency}} $$
- Therefore, $$ \text{Energy input} = \frac{45 \text{ kWh}}{0.40} = 112.5 \text{ kWh} $$
- Find out the amount of coal burned Now we need to determine how much coal is needed to generate 112.5 kWh. The average energy content of coal is about 24 MJ/kg (megajoules per kilogram). To convert kWh to MJ, we use the conversion factor that 1 kWh equals approximately 3.6 MJ.
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Hence, the required energy in MJ is: $$ \text{Energy in MJ} = 112.5 \text{ kWh} \times 3.6 \text{ MJ/kWh} = 405 \text{ MJ} $$
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Now, calculating the amount of coal needed: $$ \text{Coal required (kg)} = \frac{405 \text{ MJ}}{24 \text{ MJ/kg}} \approx 16.875 \text{ kg} $$
- Calculate the CO2 emissions from the coal burned The carbon content of coal is typically around 70%, and when burned, it produces approximately 2.67 kg of CO2 for every kg of coal consumed.
- Therefore, the total CO2 emissions are: $$ \text{CO2 emissions (kg)} = 16.875 \text{ kg} \times 2.67 \text{ kg CO2/kg coal} \approx 45.06 \text{ kg CO2} $$
The carbon footprint of the Tesla model for a distance of 300 miles using energy sourced from a coal-fired power plant is approximately 45.06 kg CO2.
More Information
This calculation shows the environmental impact of using coal-generated electricity to power an electric vehicle. The figures can vary based on local coal quality and specific energy consumption of different Tesla models.
Tips
- Failing to convert energy units correctly (kWh to MJ).
- Misunderstanding the efficiency calculation, particularly ensuring efficiency is applied in the right context (input vs. output).
- Not considering the carbon content and CO2 output ratio of the coal when calculating emissions.
AI-generated content may contain errors. Please verify critical information
