"Heat, Work & the First Law," Feature Article, March 2008

heat, work
& the first law

From Savery at the mines to Joule's propeller, the understanding of thermodynamics proceeded step by thoughtful step.

by Howard W. Butler

that energy can neither be created nor destroyed is the first law of thermodynamics and, as far as anyone can observe or theorize, the law is in force throughout the universe. Marks' Practical Handbook for Mechanical Engineers calls the first law "one of the very important laws of nature."

Thermodynamics is an engineering science that evolved piecemeal over many years and with contributions from many investigators. A basic form of the first law for simple systems states that the increase in the internal energy of a system is equal to the quantity of heat transferred to the system reduced by the quantity of work done by the system. Expressed mathematically,

As shown below, this relation is a result of the famous experiments of James Joule from which he identified heat as a form of energy having a unique equivalence to work. Using standard procedures, this expression may be extended to apply to systems with mass transport across the boundaries, and to include other forms of energy.

Thermodynamics was not recognized as a science in the early years of its development and natural philosophers of the 18th century eschewed all interest in such mundane developments as steam engines, which were the work of unschooled ironmongers. So it's appropriate that a problem in mining led to the first discoveries that developed into the modern understanding of thermodynamics.

Thomas Savery: He tried to replace horses with the energy of fire, but his engine couldn't lift high enough.

The concepts of work and energy are descendants of Isaac Newton's second law of motion stated in his Principia Mathematica Philosophiae Naturalis in 1687 as, "The alteration of motion is ever proportional to the motive force impressed, and is made in the direction of the right line in which that force is impressed," i.e. mdv/dt = F. When this is multiplied by the instantaneous velocity, v = dx/dt, the concepts of work and energy are discovered: mvdv/dt = Fdx/dt or d(mv²/2) = Fdx indicating that the work expended causes an increase in the kinetic energy of the mass.

Heat was a much more elusive concept to grasp, despite man's eons of experience with fire and weather.

An early view considered it to be a mysterious substance called phlogiston that was created by fire. When it was considered that water could be made to boil by putting the pot on hot rocks, this concept was replaced by the caloric theory of heat as a conserved fluid that flowed from hot to cold bodies. This view prevailed until the middle of the 19th century and was the nemesis of Sadi Carnot in 1825 in his famous cycle analysis. This difficulty in understanding the nature of heat delayed the development of thermodynamics as a science until 1845, when James Joule conducted his famous experiments that showed that heat was another form of energy with a precise quantitative relation to work.

Milestone Patent

In the late 17th century, an event took place that would revolutionize the way in which useful work got done and, eventually, end the use of animal and slave labor for heavy tasks. This event was the awarding by the Royal Society of a patent in 1698 to Thomas Savery for the first engine to continuously convert the heat from fire into useful work.

The idea of useful work distinguishes it from a number of earlier devices that had been made. They were toys, one-shot actions like sky-rockets, or paper designs of questionable utility.

Despite his ignorance of scientific principles, by using only empirical judgments Savery built his engine to address a serious problem. As coal and tin mines were worked to greater depths, they were constantly being flooded. Water had to be removed by horses, which were hitched to a turnstile that raised large buckets to the surface. As the depths increased, so did the cost and trouble of keeping the horses fed, shod, and healthy, so Savery designed his engine to replace them.

Redefining the engine: Patented by the Royal Society in 1698, Savery's engine was the first to continuously convert the heat from fire into useful work to pump water from deep mines.

His engine used a coal-fired steam boiler connected to a cylinder that was double-valved to a suction pipe and a discharge pipe. When the cylinder was filled with steam, it was down-washed with cold water, causing the steam to condense and form a partial vacuum, drawing water up the suction pipe. The steam supply valve was then opened and the boiler pressure forced the water up the discharge pipe for ground level disposal. This cycle of events was then repeated for continuous operation. Originally, the operation of the valves was performed by trained boys, but it soon became mechanized.

Savery might have succeeded in solving a serious problem but for one major fault in his design. With his partial vacuum, he could lift water about 20 feet, and his boilers could raise it another 30 feet. The flooding mines were down to 800 feet. Clearly, staging that many engines down the mine was impractical. He did sell a few engines to provide running water for mansions. He went out of business in 1705.

Thomas Newcomen, an ironmonger in Devon, invented an engine to address the same problem that Savery attacked. Newcomen, however, was unable to get a patent on his engine because Savery's patent covered "any means for raising water by the impellant force of fire," so he joined forces with Savery in 1712.

Newcomen's engine placed a piston (originally wood) between the atmospheric air and the steam, and connected the piston to one end of a rocking beam. The other end of the beam was connected to rods that went down into the mine as far as necessary to operate the water pumps. A second innovation was to inject cold water directly into the steam to condense it, which greatly sped up the process.

These engines had a very low thermal efficiency, but that was of little concern where coal was cheap and horse maintenance costly. The engines were so successful that they were installed in mines in England, continental Europe, and North America. One was reputed to be still operating at the end of the 19th century, and one is on display at the Henry Ford Museum in Detroit.

Enter James Watt

While restoring a Newcomen engine at the University of Scotland in 1765, James Watt discovered that some 80 percent of the steam was wasted by premature condensation on the cold walls of the cylinder. To reduce this effect, he conceived the idea of adding a small condensing chamber adjacent to the main cylinder, thus letting the walls remain at a high temperature. His next contribution was to convert the reciprocating motion of the beam to rotary motion, and Watt's engines were soon used in mills and factories.

These engines still used atmospheric pressure steam, since the boilers of the time were made of soldered copper and lead, which could not withstand high pressures and temperatures. This problem was solved with the development of tube boilers and corrosion-resistant steels, which made possible the mounting of engines on railed vehicles for land transportation, and on ships for sea travel. The future of animals and sails for these purposes was foredoomed, and the industrial revolution was launched.

Watt made other important contributions to the development of thermodynamics. While he was at the University of Scotland, he made friends with a professor of physical chemistry, Joseph Black, who was a member of the Royal Society. After many successful years in the engine business, he joined Black to conduct experiments on the determination of specific heats and latent heats. Historically, this was probably the first step that went beyond empirical improvements and introduced analytical and experimental methods in the study of thermal processes.

James Watt: Besides his improvements to the steam engine, his contributions include experimental work with Joseph Black in Scotland.

This involved the definition of the British thermal unit as the amount of heat needed to raise the temperature of one pound of water one degree Fahrenheit. It also disclosed that the specific heat, especially for gases, depended on the nature of the process. It was higher for a constant pressure test than for a constant volume test, and higher still for an elastic constraint.

In the years following Watt and Black, interest in the nature of heat and its various effects became more widespread. One of those who came close to making an important discovery was Benjamin Thompson, who was born in Woburn, Mass., in 1753. He was opposed to the American Revolution, and wound up in London after the British evacuated Boston in 1776.

There, he conducted experiments on the power of gunpowder and continued his studies on the Continent, where he was put in charge of a cannon boring factory. Working as an aide to the Prince-Elector of Bavaria, Thompson eventually earned the title of Count of the Holy Roman Empire, and adopted the name Count Rumford after a town near his birthplace.

In his observations of cannon boring, he noticed that the brass chips that left the barrel were hotter if the cutting tool was dull than if it was sharp. By collecting them in a pail of water as a crude calorimeter, he could calculate the thermal effect, but was unable to instrument the cutting tool to measure the work input.

Thompson also conducted experiments on the specific heats of solids. His experiments on the insulating properties of various materials led to his invention of thermal underwear. He later endowed a professorial chair at Harvard University and the Rumford Medals of the American Academy of Arts and Sciences and of the Royal Society. There is no record of his having returned to America.

Joule's Law

James Joule was born in Manchester, England, in 1818 and became fascinated with electricity at an early age. In 1840, he discovered what is universally known as Joule's Law—i.e., E = I²R, where E is the rate at which electric energy is dissipated when an electric current passes through a resistance, which was clearly in conflict with the prevailing caloric theory.

In 1845, Joule devised a simple apparatus that made it possible to determine the equivalence of heat and work. The earlier work on specific heats had defined the Btu unit of heat, and Joule defined what he called the "economic duty" of a device as the ability to raise one pound to a height of one foot, i.e., one foot-pound.

His apparatus consisted of a well-insulated rigid chamber containing a viscous fluid and fitted with a rotating propeller instrumented so that he could precisely measure the work required to drive it. He observed that for a given fluid, a definite amount of work expended always caused a definite rise in temperature of the fluid. In modern terms, he discovered the property internal energy, U, but he bypassed this step since the work on specific heats related the rise in temperature to a definite amount of heat.

Joule's best data showed that for each foot-pound of work expended, the fluid temperature rose by the same amount as it would if 0.001295 Btu of heat had been added. To avoid using such a small number, he used its reciprocal, 772.355, which is engraved on his tombstone in Manchester, and is within less than 1 percent of the accepted number, 778 foot-pounds per Btu.

James Joule: Experiments involving an instrumented propeller in a viscous fluid established heat as transformable energy.

Joule's experiment established heat as transformable energy. The mathematical expression of the first law is the result of Joule's work with the usual sign conventions and with all terms expressed in the same units. It is essentially a statement of the conservation of all forms of energy.

The physical process involved in Joule's Law is thermodynamically identical to that involved in his thermal fluid experiment. Consider a thermally insulated length of wire having a resistance and conducting an electric current. The rate at which the electric energy is dissipated into internal energy of the wire results in a definite rise in its temperature for a given time of operation.

In the equivalent thermal fluid experiment, the rate at which the mechanical energy is dissipated into internal energy of the fluid results in a similar rise in temperature of the fluid for a given time of operation. Thus, the electric resistance of the wire plays the same role as the viscosity of the fluid in causing the energy dissipation. In each case, the magnitude of the temperature rise for a given energy dissipation is determined by the specific heats of the substances. If the thermal insulation is removed, each process would reach a steady state, where the rate of energy dissipated would be matched by the rate of heat transferred to the environment, and the second law of thermodynamics would determine the rate of entropy creation by the irreversible processes.

The Last Word

In several fields of science, major discoveries were made by single creative geniuses like Isaac Newton, Sadi Carnot, and Albert Einstein. In other fields, progress took a slower track and combined the contributions of many investigators.

Classical thermodynamics is such a field, and nothing of significance has been added to it since 1878, when Willard Gibbs published his famous paper, "On the Equilibrium of Heterogeneous Substances." This work extended the contributions of his predecessors to include chemical reactions and multiphase systems, and formed the foundation for the establishment of the modern chemical industry. The economic value of his work is beyond measure, yet he taught at Yale University for 20 years with no salary, living with his sisters and father, who was a professor of theology. He earned spending money by selling real estate in New Haven.

Gibbs was awarded the first Ph.D. in mechanical engineering ever given in the U.S., with a dissertation on the properties of involute gear teeth.

The world is rapidly approaching a crisis in the field of energy, as worldwide demand for fossil fuels continues to stress a diminishing supply. The impending shortfall has led to numerous investigations into alternate sources of energy, such as solar, geothermal, and biological, each having serious political implications when extended to effective scale. Global warming further complicates the economic and social aspects of the problem.

Since all approaches to deal effectively with these issues must satisfy the laws of thermodynamics, perhaps a better communication between policy-makers and thermodynamicists could lead to sound solutions.

for further reading

Mechanical Engineering has published numerous articles on the history and development of steam power.

Among them is "Harnessing the Void," by Robert O. Woods, an ASME Fellow. The article, published in December 2003, discusses the development of Thomas Newcomen's steam engine.

Franks Wicks, also an ASME Fellow, wrote "Pressure's On," which appeared in the October 2007 issue. He argues that the introduction of the first commercially successful steamboat by the partnership of Robert Fulton and Robert Livingston was a major contribution not only to the economy of the time, but also to the mechanical engineering profession.

Howard W. Butler's article on the development of the second law of thermodynamics, "Tracing the Second Law," was published in the July 2007 issue of the magazine.

Howard W. Butler is a former professor of mechanical engineering at Rensselaer Polytechnic Institute and a retired chairman of the Department of Mechanical Engineering at West Virginia University.