$CO_2$ Production by Automobiles

by Jeffrey Kantor (jeff at nd.edu). The latest version of this notebook is available at https://github.com/jckantor/CBE20255.

Summary

This Jupyter notebook demonstrates the solution of a mass balance for a vehical powered by an internal combusion engine.

Problem Statement

Part a.

A recent model automobile is advertised with a fuel consumption of 30 miles per gallon of gasoline. Assume gasoline consists of pure octane $C_8H_{18}$, has a specific gravity of 0.74, and is consumed via the chemical reaction

$$C_8H_{18} + \frac{25}{2}\ O_2 \longrightarrow 8\ CO_2 + 9\ H_2O$$

How much $CO_2$ is generated per mile driven? Report your answer in grams/mile.

Solution

In [1]:
liters_per_m3 = 1000.0
gallons_per_m3 = 264.17

V_lpm = (1.0*liters_per_m3/gallons_per_m3)/30.0      # volume of gasline in liters/mile
m_kg = 0.74*V_lpm                                    # mass of gasoline in kg/mile
m_grams = m_kg*1000.0                                # mass of gasoline in grams/mile
n_octane = m_grams/114.0                             # moles of gasoline in gmol/mile
n_co2 = 8.0*n_octane                                 # modles of CO2 in gmol/mile
m_co2 = 44.0*n_co2                                   # mass of CO2 in grams/mile

print("Gasoline consumed per mile = ", round(m_grams,1), "g/mile")
print("Gram moles of octane per mile = ", round(n_octane,3) ,"gmol/mile")
print("CO2 Production =", round(m_co2,1), "g/mile")
Gasoline consumed per mile =  93.4 g/mile
Gram moles of octane per mile =  0.819 gmol/mile
CO2 Production = 288.3 g/mile

Part b.

Owners of the Tesla S electric car report an average electricity consumption of 0.367 kilowatt-hours per mile driven.

Assume the electricity is produced from natural gas which, according to the U.S. Energy Information Administration, produces 117.0 pounds of $CO_2$ per million BTU consumed, and requires 10,400 BTU to produce a kilowatt-hour of electricity. Assume an overall transmission efficiency of 80% from the power plant to the Tesla motor. How many grams of $CO_2$ are generated per mile driven by the Tesla?

Solution

In [2]:
grams_per_lb = 453.593

w_kwh = 0.367                     # kwh per mile
q_btu = (w_kwh/0.8)*10400.0       # natural gas per mile

print("Thermal energy requirement =",round(q_btu,2),"BTU per mile driven")
Thermal energy requirement = 4771.0 BTU per mile driven
In [3]:
m_co2_lb = 117.0*q_btu/1.0e6           # mass CO2 lb/mile
m_co2_grams = m_co2_lb*grams_per_lb    # mass CO2 grams/mile

print("CO2 Production =", round(m_co2_grams,2), "grams per mile")
CO2 Production = 253.2 grams per mile