1. The IPAT Equation Use the IPAT equation to estimate the percentage increase in the amount of energy that would be required, worldwide, in 2050, relative to 2006. To estimate the increase in population and affluence (the P and A in the IPAT equation), assume that population grows 1% per year and that global economic activity per person grows 2% per year. Assume that the energy consumption per dollar of GDP (the T in the IPAT equation) remains at 2006 levels. How much does this estimate change if population growth is 2% and economic growth is 4%? (20 points)

No. of years = 2050-2006 = 44 years

Energy required, I = PAT

I₂₀₅₀/I₂₀₀₆ = (P₂₀₅₀/P₂₀₀₆)*(A₂₀₅₀/A₂₀₀₆)*(T₂₀₅₀/T₂₀₀₆)

= (1.01)*(1.02)*1)

For 44 years, I₂₀₅₀/I₂₀₀₆ = 1.01⁴⁴*1.02⁴⁴*1 = 3.7029

which means an increase of 3.7029-1 = 270.29%

 

 

For second case,

For 44 years, I₂₀₅₀/I₂₀₀₆ = 1.02⁴⁴*1.04⁴⁴*1 = 13.4238

which means an increase of 13.4238-1 = 1242.38%

 

 

 

2. Estimate the amount of energy that will be used annually, worldwide, if over the next 50 years world population grows to 10 billion and energy use per capita increases to the current per capita consumption rate in the US (330 million BTU/person/yr). What percentage increase does this represent over current global energy use (450 quads)? (20 points)

Energy used will be 10 billion*330 million BTU/person/yr = 3300 Quadrillion BTU

Percentage increase = (3300-450)*100/450 = 633.33%

 

3. Assume that the conversion of energy into mechanical work (at the wheel) in an internal combustion engine is 20%. Calculate gallons of gasoline required to deliver 30 horsepower at the wheel, for one hour. (20 points)

1 HP = 746 Watts

1 HP for 1 hour is 0.746 kWh

1 Kwh = 3412 BTU

So, 1 HP = 0.746 kWh * 3412 BTU/kWh = 2545 BTU

Gallons of gasoline required = 2545*(1/124000)*(1/0.2) = 0.1 gal

4. Assuming that generating a kilowatt hour of electricity requires an average of 13 gallons of water (Example 1.4-3) and that an average electric vehicle requires 0.3 kWh/mi traveled (KintnerMeyer, et. al., 2007), calculate the water use per mile traveled for an electric vehicle. If gasoline production requires approximately 10 gallons of water per gallon produced and an average gasoline powered vehicle has a fuel efficiency of 25 miles per gallon, calculate the water use per mile traveled of a gasoline powered vehicle. (20 points)

 

For electric vehicle, water use per mile = 0.3*13 = 3.9 gal/mi

For gas vehicle, water use per mile = 10*1/25 = 0.4 gal/mi