Introduction

Heat, Energy, and Work all have the same units of a joule. However, each has its own unique definition. Heat and work are path functions whereas energy is a state function. Each of these are used in thermodynamic and it is important to understand both their differences and how they are related.

History of James Joule

James Joule studied physics throughout the mid-1800s. In the 1840s, he used a paddle wheel attached to a falling weight to measure the change in temperature produced by the friction. From this Joule determined the mechanical equivalent of heat. He also made the conversion from Joules to calories following this test (1 cal=4.15 J), which is close to today’s accepted conversion (1 cal=4.184 J). his experiments helped develop the Law of Conservation of Energy and showed that heat is produced by motion, contradicting the caloric theory*. In addition, Joule discovered that the heat dissipated by a resistor is equal to Q=I2Rt where I is current, R is resistance, and t is time. This became known as Joule’s Law.

*The caloric theory stated that heat is a fluid that is conserved and transferred from body to body.

Laws of Thermodynamics

The First Law of Thermodynamics is commonly referred to as the conservation of energy, meaning that energy is neither created nor destroyed, and the total amount of energy remains constant. The total energy is the sum of kinetic, potential, and internal energy, given by ETotal=KE+PE+U. It is important to note that KE and PE are the kinetic energy and potential energy of macroscopic systems and U contains the kinetic energy and potential of the microscopic systems/atoms. For a closed system, the change in internal energy is the sum of heat and work, given by ∆U=q+w. For an isolated system, ∆U=0.

The Second Law of Thermodynamics deals with entropy. Isolated systems consistently move toward thermodynamic equilibrium (the state of maximum entropy of the universe), so the entropy in an isolated system does not decrease. No system can be 100% efficient because it cannot exceed the fundamental limit of thermodynamic efficiency. To calculate the change in entropy in a system, find the difference of the initial and final state of entropy, given as ∆S=Sf - Si.

The Third Law of Thermodynamics includes the relationship of entropy and temperature. For any pure substance in equilibrium, as temperature approaches absolute zero, the entropy approaches zero.

**System vs Surroundings**

For every thermodynamic problem there are two areas that are defined in space: the system and the surroundings the envelop that system. Certain assumptions are associated with each term.

System: A system is a small part of the universe that is being studied by an observer. In comparison to the surroundings, a system has very finite describing quantities (such as internal energy, volume, and temperature), atomic makeup, and has well defined walls that separate the system from everything outside of the system. While these walls don't have to be physical walls they must be well defined (for example, a certain volume of outer space can be contained within imaginary walls to define a system as long as the volume is definite).

- Closed System - A system that can only exchange heat and work with its surrounding, but cannot exchange matter
- Isolated System - A system that is completely isolated is on that cannot exchange heat, work, or matter with its surroundings.
- Isobaric Change - A change in a system that occurs under constant pressure
- Isothermal Change - A change in a system that occurs under constant temperature
- Isochoric Change - A change in a system that occurs under constant volume

Surroundings: Surroundings define anything that exists outside of the bounds of the system. This includes energy (in the form of light, heat, potential for work, etc.) and matter that may be transferred into the system. Surroundings are always bigger than the system.and do not include the state of energy and matter within the system. However, surroundings are important to understand in relation to the system because they represent the source of external forces that act on the system and cause changes in the system’s properties.

Figure 1. A diagram simplifying how to determine signs of work and heat.

Definition of Heat, Energy, and Work

- Heat and work are different from the concept of energy because heat and work are processes of changing the internal energy of a system. As a result, all three of these have the same unit. We consider heat and work as different processes because they have different methods for exchanging energy.

- Heat is the transfer of energy between two objects that are at different temperatures. This energy transfer speeds up the individual atoms/molecules at the microscopic level. Heat is related to the mass, specific heat, and the change in temperature of an object. Specific heat is defined as the amount of energy per unit mass to raise a substance's temperature by 1 degree Celsius. *q=m*cs*∆T *When there is an increase in the temperature, q is positive which denotes that there is energy being added to the system. When there is a decrease in temperature, q is negative which denotes that energy is being taken away from the system.

- Work is the transfer of energy to cause an object to move a distance at the macroscopic level. *W=F*d* where d is the distance that the object traveled and force is the amount of force applied in the direction of movement. When force opposes the direction of movement, there is negative work (loss of energy from the system). For a gas,** ***W = -P∆V.*

*W = F*d*

In gases, *P=F/A --> F=PA* and* d* = change in height of cylinder.

*W=-PA*Δh *Pressure is negative because it opposes the direction of movement

*W=-P(A*Δh)*

*W=-P*ΔV*

- Temperature is often confused to be the same as energy, heat, and work. Temperature is a measure of how fast molecules move. It is proportional to the average kinetic energy in a substance. As a result, temperature is related to both heat and energy. In fact, if you look below to Calorimetry, the equation for heat includes temperatures as one of the independent variables. It is also interesting to note that work CAN also change temperature. Putting work on a system can increase its energy and if the systems kinetic energy is increased, then the temperature will also increase.

One problem many students experience in relation to these topics is that the words “heat”, “temperature”, and “energy” are often used in everyday language in different ways than how they are used in a scientific context. For example, a common misconception that many students experience in their everyday lives implies that work and heat are interchangeable. Microwave ovens work by using microwave radiation to cause rotational movement in water molecules. While it is common to say that someone is “heating up” something in a microwave oven, this process does not actually involve heat at all. The energy in the waves does work on the water molecules in the food being heated, which causes an increase the average kinetic energy of the water molecules (and thus an increase in temperature). While it was the idea of work that was most helpful in making last night’s leftovers palatable, the misconception of interchangeable heat and work largely remains in society.

Enthalpy

In the 19th century, H was commonly used to denote heat. Enthalpy is a state function that is very strongly related to heat and as a result, it was given the symbol H. Enthalpy is a state function described as *H=U+PV*. Change in enthalpy is directly related to heat when pressure is constant.

*∆H=∆U+P∆V*

∆U = q_{p}+w = q_{p }-P∆V

*Therefore**, q*_{p} = ∆U + P∆V = ∆H at constant pressure

* ** *

The change in enthalpy is an important function because it tells us the amount of energy that is released or absorbed in a reaction. This is why it is also considered the "heat of the reaction" because it explains how much heat is required/released in a reaction. It is important to note that ∆H = q_{p }only when pressure is constant. When pressure is not constant, the following formula applies: **∆H=∆U+∆(PV).**

The Mathematical Approach to Energy, Work, and Heat

Heat Capacity (JK-1)

It is defined as the amount of energy required to change a substance’s temperature by 1 degree Kelvin. However, this is not a constant value, as there are parameters that affect this value: volume and pressure. The formulas are here:

Figure 2. Equations for heat capacities for monoatomic gases. These are the equations for the heat capacity of a system with constant volume and pressure, respectively.

The first formula means that the heat capacity at a constant volume (C_{V}) is the partial derivative of internal energy with respect to temperature. This shows that this type of heat capacity is related to the rate of how internal energy changes based on temperature. Also, there is no change in volume, resulting in no work being done on the system. Therefore, the change of internal energy revolves around heat. Since only heat is related to the internal energy, it shows that C_{V} can be called energy capacity of the system.

The second formula is for the heat capacity at a constant pressure (C_{P}), which is the partial derivative of enthalpy with respect to temperature. For this case, the volume is not constant, so work can be done by or on the system. With this extra factor, it is important to note that the value for CP is always greater than C_{V}. This rule is applicable to all systems. Similar to C_{V}, C_{P} has another name, enthalpy capacity. This is true because C_{P} is related to enthalpy of a system.

There is also another version, where it is molar heat capacity, which basically means how much energy is needed to raise a mole of a substance by one degree Kelvin. The formulas show that the difference between the two molar heat capacities is R, the gas constant.

It is important to note that these equations only apply to monoatomic gases. For a polyatomic gas, you must take into account the degrees of freedom a molecule has. The equation would be as follows:

*C*_{v}= F/2 * R (Where F is the number of degrees of freedom)

*C*_{p} = C_{v} + R

Calorimetry

Calorimetry is a way to study how a system changes temperature. It is also applied to measure the amount of heat that is produced or absorbed by a physical or chemical process. There are two types of calorimetry - bomb calorimetry and coffee-cup calorimetry. These correspond to constant volume settings and constant pressure settings, respectively. The formulas needed for this computation are:

*q*_{bomb} = ∆U = C_{V}∆T

*q*_{coffee}= ∆H = C_{P}∆T

Additionally, the following image can help understand the concept of a bomb and coffee cup calorimetry:

Figure 3. The calorimeters used in thermodynamics. A. is for coffee cup calorimery. This keeps the system at a constant pressure since it is equivalent to the surroundings. B. is for a bomb calorimeter. This keeps the system from changing volume for a certain type of study.

These formulas uses concepts stated in the previous section, and this is an application that is widely used to study reactions and other processes of interest. It is also important to note that these systems are isothermal with the surroundings outside of the calorimeter. Otherwise, readings and results of this technique would be flawed.

Summary

There are nuances that distinguish the definitions of energy, heat, and work. These also have different ways of being derived and expressed. These concepts are relevant to the world because there is energy, work, heat, and enthalpy all in the universe, and these concepts are all related to one another. The universe is just one big system that has many systems within itself. It is also important to note calorimetry as a great tool to solve for these concepts in relation to physical and chemical processes. Understanding these concepts on a microscopic level can also help one understand many other concepts on the macroscopic level.

Concept Questions

1) Which of the following is a correct statement?

a) Heat is a state function, Internal Energy is a path function, Work is a state function

b) Heat is a path function, Internal Energy is a path function, Work is a path function

c) Heat is a path function, Internal Energy is a state function, Work is a path function

d) Heat is a state function, Internal Energy is a state function, Work is a state function

2) Isothermal, Isochoric, and Isobaric reactions correspond respectively to reactions that have __________ throughout the course of the reaction:

a) the same temperature, the same number of mols, the same volume

b) the same temperature, the same volume, the same pressure

c) the same temperature, the same number of mols, the same pressure

d) the same number of mols, the same pressure, the same volume

3) Which of the following statements describe an Ideal Gas? (choose all correct answer(s))

a) The interactions between molecules are negligible

b) Molecules of gas are assumed to collide inelastically

c) Mean Free Path is assumed to be large

d) R = 8.3145 J/(Kmol) or .08206 Jatm/Kmol

References

Joule, James (1818-1889). (n.d.). In Eric Weisstein’s World of Physics. Retrieved from

http://scienceworld.wolfram.com/biography/Joule.html.

Caloric Theory. (n.d.). In Eric Weisstein’s World of Physics. Retrieved from

http://scienceworld.wolfram.com/physics/CaloricTheory.html.

http://adsabs.harvard.edu/abs/2002JChEd..79..697H

http://www.chm.davidson.edu/vce/calorimetry/heatcapacity.html

http://www.science.uwaterloo.ca/~cchieh/cact/c120/calorimetry.html

Answers to Concept Questions

1) C

2) B

3) A,C (D is incorrect; watch units!)

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