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Units of Energy and Specific Heat
bottled water

You may remember from the metrics tutorial that distance, mass, and volume were based on water. The same is true with some units of energy. This liter bottle will help illustrate these units. If you took the bottle and threw it so that it took one second to make the throw and the bottle was traveling 1 meter per second speed as you let it go, one "joule" of energy was transferred to the bottle. (Joule is named after James Joule) The force that you exerted on the the kilogram of water to get that liter of water up to 1 meter per second is defined as one "newton" of force (Symbol is N). Energy is often calculated as force times distance. So in this case, one newton of force times one meter is called either newton·meter or one joule.

pen light A joule also is related to electricity. One watt (about the power or a penlight) is consuming one joule per second. A watt (1 joule per second) is a measurement of power. Power is a certain amount of energy produced or consumed per unit of time.
light bulb held
A 15 watt light bulb therefore consumes 15 joules per second. That means it could accelerate 15 liters (about 4 gallons) of water up to 1 meter per second every second. Therefore in 60 seconds those 4 gallons of water will be traveling at 60 meters per second (122 miles per hour). So even a dim 15 watt bulb is consuming a lot of energy.

Another unit of energy based on water is the calorie. A calorie is defined as the amount of energy needed to raise 1 gram of water 1 degree Celsius. If it is a kilogram of water (1 liter), they call that a kilocalorie or a food calorie.

In this example. we have a kilogram of water. That would take 1,000 calories to raise it 1 degree Celsius. If going from room temperature (20°C) up to near boiling (90°C), that's a 70 degree increase and therefore 70 x 1000 calories, or 70,000 calories to heat it.

hamburger
Again, food calories are actually 1000 calories. This hamburger is said to be 1,000 calories, but it's actually 1,000,000 calories. Food calories are supposed to be written with a capital "C". So the hamburger is 1,000 Calories or 1,000,000 calories.
Grill
When buying heaters, air conditioners, and barbeque grills, you often see it rated in BTU. That stands for British Thermal Units. This is similar to calories because it is based on the energy to heat water. But instead of metric units, it uses English units. A BTU is the energy needed to raise one pound of water 1 degree Fahrenheit. A pound is 454 grams of water and a Fahrenheit degree is 5/9 the size of a Celsius degree. So that means one BTU equals 454x5/9 or 252 calories. Often they rate these items in BTU but they actually mean BTU per hour, which is the rate of heating or cooling. This grill was listed as 48,000 BTU grill. That means it puts out 48,000 BTU of energy per hour. So it could raise the temperature of 1,000 lbs of water 48°F each hour. That's a lot of heating.
Another energy unit that we are all familiar with is the kilowatt·hour, which is how the electric companies charge us for electrical energy. You just learned that a watt is 1 joule per second. A kilowatt therefore is 1000 joules per second. Kilowatt·hour is a kilowatt of power being used for one hour. These are multiplied. That shows that 1 kilowatt hour is 3.6 million joules.
 
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1                    
2
1
kilowatt·hour
1
joule/sec 1000
3600
sec
=
3600000
joules
3    
1
watt kilo
1
hour      
1 calorie is equal to 4.18 joules. So multiply this answer by 1cal/4.18 joules and we get 861,000 calories, which is only 861 food Calories. So a hamburger has about the same energy as running a 1 kilowatt toaster for one hour.
Specific Heat
The definition of a calorie as the energy to raise one gram of water one degree Celsius leads us to a property of water known as "Specific Heat". That property says that water requires 1 calorie for each gram of water present and each degree Celsius that those grams of water heat up. Other materials require a different amount of calories to heat up.

For example, the specific heat of gold is over 30 times smaller than that of water. In other words, a kilogram of gold will go from 20°C to 90°C, while water will only go from 20°C to 22°C when they both are heated equally. The specific heat of gold is 0.031 calories per gram per degree Celsius (0.031cal/g·°C).

Why such a big difference? (See next paragraph(

water charges It has to do with the heat being stored as kinetic energy (atoms and molecule moving faster) and energy being stored as potential energy (plus and minus charges being separated). You know that water is polar with + and - ends. As water heats up the molecules move away from this aligned arrangement where the + and - charges are close to each other. Having the charges farther away stores more potential energy. It's likes stretching a rubber band. There's energy there as they snap back into their more stable (lower energy) alignment position.
Each metal and each material have a different rate of heating. Here we see that gold heats up 7 times faster than aluminum. That means that everything has their own specific heat (also called heat capacity). Aluminum's specific heat is 0.216 cal/g·°C, which is about 7 times more than that of gold (0.031 cal/g·°C).
There was an episode of Mission Impossible TV show in the 70's that utilized that fact that gold heats up so quickly compared to other materials. They drilled a hole in the bottom of a vault and inserted an electric heat rod. The gold in the vault heated up quickly. So it melted and ran out the hole in the bottom of the vault before any of the paper money or other coins got too hot. I'm not sure that would really work, but the low specific heat of gold makes it possible.
One way to determine the specific heat of a substance is to heat it along side an equal mass of water. If the water heated up 8 degrees and the substance heated up 1 degree, then that substance has a specific heat of 1/8 of that of water. So its specific heat would be 0.125cal/g·°C
blacksmith

A more common approach to find the specific heat of a substance (like metals) is to heat that substance and then put it into a known amount of water.

The blacksmith may have been one of the first people to recognize this. They often drop various metals into a bucket of water to cool the metal. They undoubtedly noticed that the water would heat up. They knew the heavier the piece of metal, the more the water would heat up. They may have noticed that different metals of equal weight would not heat up the water to the same temperature.

As we would suspect a hot iron horseshoe dropped into this water will heat up the water at the same time as cooling off the horseshoe. Also, in a minute or so, the horseshoe and water will be the same temperature.

By knowing the mass of the horseshoe, the mass of the water, plus the beginning temperatures of the water and horseshoe, along with the final temperature of the water, we can figure out the specific heat of iron.

The trick to figuring this out is to recognize that the energy lost by the horseshoe will be the energy gained by the water. In other words the calories lost is equal to the calories gained.

Specific heat is calories per gram per degree Celsius. That means if we multiply by grams and degrees Celsius, those units cancel and we are left with just calories (energy)

Let's say this horseshoe weighed 449 grams and was 455°C before dropping into the water. There were 2.00 liters (2,000g) of water, which started out at 24°C and ended up at 34.2°C. What is the specific heat of iron?

Again, we set up an equation that shows the energy lost by the iron equals the energy gained by the water.

Notice in the spreadsheet below that the one °C in the denominator cancel both of the °C in the numerator because after those in the numerator are subtracted, there's only one °C left.

In row 5, the calculations in row 2 were done and the results were written. Notice the negative sign in front of the loss of heat from the iron. That negative sign will cancel the negative sign when 455°C is subtracted from 34.2°C.
 
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Energy lost from the horseshoe
equals
Energy gained by the water
1
unknown specific heat
mass iron
Final Temp
 
Initial Temp
 
specific heat water
mass water
Final Temp
 
Initial Temp
2
-
???
calories
449
g
34.2
°C
-
455
°C
=
1.00
calories
2000
g
34.2
°C
-
24.0
°C
3
  g·°C                   g·°C              
4      
Formula in I5 is "=D2*(F2-I2)"
  Formula in L5 is "=N2*(P2-T2)"        
5      
-
???
calories
x
-188939
g·°C
=
20400
calories              
6             g·°C                          
7          
Solving for unknown specific heat by dividing both sides by 188939 g·°C
         
8    
Formula in I8 is "=L8/L9" 
0.108
calories
=
20400
calories Formula in L8 is "=L5"
9                   g·°C  
188939
g·°C Formula in L9 is "=I5"

Here we get the specific heat of the iron in the horseshoe as 0.108 calories per g per °C. If this is entered in a spreadsheet, you can change any of the values in row 2 and the specific heat will automatically be calculated in I8.

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Since Oct 29, 2009