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 Q=mCΔT can be used to solve many problems involving heat capacities. Q represents the amount of heat supplied to the system. 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 Q=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 Q=mCΔT. Q=100 J, m= 3 g, ΔT=3 °C. 100J= (3 g)*(C)*(3 °C). C=11.11111 J/g °C.

Connectedness

1. 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.
2. 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.
3. Chemical Engineers use knowledge of heat capacity and specific heats to make sure that processes run safely and efficiently.

History

Thermodynamics was brought up as a science in the 18th and 19th centuries. However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer. G. Black first introduced the word 'thermodynamics'. Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat. The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot. He is often known as "the father of thermodynamics". It all began with the development of the steam engine during the Industrial Revolution. He devised an ideal cycle of operation. During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics. In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics. Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium.

See also

• Specific Heat
• Thermal Energy

Further reading

Elementary Principles of Chemical Processes (3rd Edition) By: Richard M. Felder & Ronald M. Rousseau

Encyclopædia Britannica, 2015, "Heat capacity"

References

• http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/Calorimetry/Heat_Capacity
• http://www.chm.davidson.edu/vce/calorimetry/heatcapacity.html
• http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html