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

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")
```

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")
```

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")
```