# Problems about energy and dimension (checking my solutions)

1. Sep 29, 2015

### TheMathNoob

1. The problem statement, all variables and given/known data

Hence no one in the science section helped me I decided to come here. Anyways, the problems are just basic math.

1 )A gallon of gasoline carries with it about 1.3*10^8 J of energy. Given a price of $3 per gallon, how many Joules can you get for a dollar? 2)Electricity goes for about$0.05 per kilowatt hour. A kilowatt hour is just a weird way to write Joules because a watt is a joule per second, and a kilowatt hour is the number of Joules one would get from running 1000 W times one hour (3,600 seconds). In the form of electricity, how many Joules can you get for a dollar?

3)A standard cubic foot of natural gas carries with it about 1.1 x 106 J of energy. You can get about 5 x 105 British thermal units(BTUs) of gas for a dollar, and there are about 1,030 BTUs in a standard cubic foot. How many Joules of energy in the form of natural gas can you get for a dollar?

4)A ton of coal holds about 3.2 x1010 Joules of energy and costs about $40. How many Joules of energy in the form of coal can you get for a dollar? 5)Corn oil costs about$0.10 per fluid ounce wholesale. A fluid ounce carries about 240 dietary calories (which a scientist would call kilocalories). A calorie is about 4.2 Joules. How many Joules of energy in the form of corn oil can you get for a dollar?

6)Rank these as energy sources,cheap to expensive. What is the ratio in cost per Joule between the most expensive and the cheapest form?

2. Relevant equations

3. The attempt at a solution
1) 1.3*(10^8)/3= 4.3*10^7
2)kw*h=1000w*3600s=1000J/s*3600s=3.6*10^6J
so electricity goes \$0.05/3.6*10^6 J
for 1 dollar= 20*3.6*10^6 J=7.2*10^7 J
3)(5*10^5 BTUS/ 1030 BTUS)*(1.1*10^16)= 5.3*10^8 J
4)(3.2*10^10)/40 = 8*10^8
5) 240KC*1000C/1KC*4.2=1.008*10^7
6 Coal, natural gas, electricity,gasoline, corn oil
Based on the choices, Corn coil is about 10 times more expensive than coal.

2. Sep 29, 2015

### HallsofIvy

Staff Emeritus
Those are correct but, for the last, you say that with coal you get 4.3x 10^7 Joules per dollar and with corn oil 1.008 x 10^7. That's a ratio 4.3/1.008. Corn oil appears to be about 4 times as expensive, not 10 times. How did you get 10 times?

Ignore this last statement. For some reason, I was thinking the first and last, most efficient and least, were being compared but now I see that coal was just before corn oil.

Last edited: Sep 30, 2015
3. Sep 29, 2015

### TheMathNoob

For coal I get 8*10^8.

4. Oct 1, 2015

### haruspex

Ok, but that still does not give 10 times.

5. Oct 3, 2015

### TheMathNoob

Yes, it's like 80 times

6. Oct 3, 2015

Agreed.