Heat Capacity
Claimed by Adam Schatz
Heat Capacity
The concept of Heat Capacity is integral to understanding how the temperature of a substance rises and falls. Heat Capacity is the ratio of energy added or removed from a substance to the temperature change observed in that substance. Typically, heat capacities are expressed in terms of the amount of heat (kJ, J, or kCal) that needs to be added to raise the temperature of a substance by 1 degree (Celsius, Fahrenheit, Kelvin). Typical units of Heat Capacities are J/g, kJ/kg, and BTU/lb-mass. The SI unit of heat capacity is J/g.
Various Types of Heat Capacities
Specific Heat Capacity
A specific property is an extensive property divided by a specific amount. Therefore, the Specific Heat Capacity of a substance tells you the amount of heat needed to one mass unit of substance one degree. Specific heat capacities are useful for determining the exact amount of heat that must be added to raise some exact amount of substance to some exact temperature. For instance, if you wanted to figure out how much heat was lost from 20 kg of water cooling from 30°C to 25°C, the calculation would involve specific heat capacities.
Molar Heat Capacity
Molar heat capacity is similar to specific heat capacity. It expresses the amount of heat required to raise one gram-mole of a substance by one degree. It is expressed in J/mol-°C. The molar heat capacity of water is 75.37 J/mol-°C.
Heat Capacity at Constant Pressure
Most of the time when heat capacity is mentioned, the heat capacity at constant pressure (Cp) is what is being referred to. This is simply, the ability of a substance to store heat at constant pressure.
Heat Capacity at Constant Volume
In some practical applications, the heat capacity at constant volume (Cv) is needed. This is similar to the heat capacity at constant pressure, but is at constant volume and variable pressure. Most of the time this is only seen in closed systems where the volume can be easily fixed.
For liquids and solids, the heat capacity at constant pressure and heat capacity at constant volume are roughly equal. For Ideal Gases, Cp = Cv+R, where R is the ideal gas constant.
Calculating/Estimating Heat Capacities
Kopp's Rule
Kopp's rule is a simple way to estimate heat capacities of liquids or solids around room temperature. To estimate Cp for a molecular compound, one can simply sum the contributions of each element in the compound. The chart below is used for Kopp's Rule.
Converting from Specific Heat Capacity to Heat Capacity
Specific heat capacity is an intensive property, which means it doesn't depend on how much of a substance is present. Conversely, heat capacity is an extensive property, which means that it does depend on the amount of substance present. In other words, the specific heat capacity for 1 kg of iron is the same as 100 kg of iron, but the heat capacity would be different for these two amounts, since it takes more heat to raise 100 kg of iron by one degree than it does to raise one kg of iron by one degree. To determine the heat capacity of a quantity of substance, simply multiply the specific heat capacity by the amount of substance present.
Applications
Using Heat Capacities
The equation ΔEthermal=mCΔT can be used to solve many problems involving heat capacities. ΔEthermal represents the the change in thermal energy of the substance. If no work is done on the substance, ΔEthermal can be assumed equal to Q which is the amount of heat supplied to the substance. m is the mass of substance present. C is the specific heat capacity. ΔT is the desired/observed temperature change. As long as 3 of the 4 quantities are known, the last can be determined.
Examples
Problem: You have a burner that emits 15,000 J of heat in the period that it is left on. Will this burner be able to raise 2 kg of water from 50 °C to 52 °C? The specific heat capacity of water is 4,186 J/kg °C.
Solution: Use ΔQ=mCΔT. The amount of heat needed to do the process specified in the question is Q=(2 kg)*(4,186 J/kg °C)*(2 °C)=16,744 J. Since the burner only gives of 15,000 J, the water will not reach the desired temperature.
Problem: What is the specific heat of 3 g substance that takes 100 J to raise 3 degrees.
Solution: Use ΔQ=mCΔT. Q=100 J, m= 3 g, ΔT=3 °C. 100J= (3 g)*(C)*(3 °C). C=11.11111 J/g °C.
Connectedness
- I am really interested by cooking. This topic has many applications in cooking. For instance, since different materials have different heat capacities, some materials make better cooking utensils than others. You wouldn't want a spatula made out of a material with a low specific heat capacity because it could easily melt and ruin your food! Also, knowing the basics of heat capacity can help you predict how long it will take for water to boil which could make cooking more efficient.
- My major is Chemical and Biomolecular Engineering. This topic has a lot of connectedness to my major. This semester I took the intro ChBE class, and the entire second half of the class dealt with energy balances. Problems involved figuring out how much heat was gained or lost by/from a system when a reaction took place. Because inlet and outlet temperatures were often not at the tabulated reference states for many chemical species, I would often have to use my knowledge of specific heat and heat capacity to figure out enthalpy changes.
- Chemical Engineers use knowledge of heat capacity and specific heats to make sure that processes run safely and efficiently.
History
Before the creation of modern thermodynamics in the 18th and 19th centuries, many scientists believed heat to be an an amount of an invisible fluid that different systems held. However since developing thermodynamics, scientists now understand heat to be the measure of the change of a system's internal energy or microscopic kinetic energy.
See also
Further reading
Elementary Principles of Chemical Processes (3rd Edition) By: Richard M. Felder & Ronald M. Rousseau
Encyclopædia Britannica, 2015, "Heat capacity"