Specific heat is a measure of how much heat can be stored in a substance. It is defined as the amount of energy needed to raise one gram of a substance by one Kelvin. Originally, the unit of energy was the calorie. A calorie is the amount of energy needed to raise the temperature of one gram of liquid water by one Kelvin (or one degree Celsius). Specifically, the temperature rise was to be 14.5 to 15.5 degrees Celsius. After the SI convention was established, however, the joule replaced the calorie. Today, the specific heat of a species is expressed in joules per gram times Kelvins, or J/g * K. Since the specific heat of water in joules is 4.184 J/g * K, one calorie is equal to 4.184 joules.
Specific heats are useful bits of information to know, because this concept both allows one to know how much heat is needed to raise the temperature of any given substance and can be used to at least partially identify an unknown substance.
For instance, the specific heat of liquid water is 4.184 joules per gram. To raise 20 milliliters of water by 5 degrees, multiply 20 grams by 5 degrees by the specific heat, and you get an energy requirement of 418.4 joules.
Example Problem 1
Solve the problems below:
A. How many degrees will the temperature of a 63-gram sample of a substance with a specific heat of 1.672 J/g * K rise if 9000 joules are applied?
B. What is the specific heat of an element if 10 kilojoules heats a 214-gram sample by 24 Kelvins?
C. How much water is in a beaker if 130 kilojoules heats the water by 76 Kelvins?
D. How many joules are required to heat a 1-kilogram bar of aluminum (specific heat = 0.902 J/g * K) by 250 Kelvins?
A. 9000 J / ((1.672 J/g * K) * 63 g) = 85.44 kelvins.
B. Specific heat = 10000 J / (214 g * 24 K) = 1.947 J/g * K.
C. 4.184 J/g * K = 130000 J / (X grams * 76 K) => mass = 408.826 grams.
D. 0.902 J/g * K = X joules / (1000 g * 250 K) => joules = 225500 joules, or 225.5 kilojoules.
That's about all there is to specific heats! Pretty painless, right? On the next page, we will review heats of state changes (such as heats of vaporization), so you can find the energy requirement to convert a block of ice at -50 °C to steam at 150 degrees.