# The Laws of Thermodynamics

## The Four Laws of Thermodynamics

Why does time seem to flow in only one direction? Can the flow of time be reversed? The directionality of time is still a puzzle because all the laws of physics except one are applicable if time were to be reversed. As we shall see in this chapter, the second law of thermodynamics is the exception. The flow of time seems to arise from the second law.

There are four laws of thermodynamics: The second law was discovered first; the first was the second; the third was the third, but it probably is not a law of thermodynamics after all; and the zeroth law was an afterthought. We shall occupy ourselves in this chapter with the study of these laws.

## The Ideal Gas Law

The study of thermodynamics is intimately connected with the study of the behavior of gases. The reason is that gases, being much simpler, are better understood than liquids and solids. An ideal gas is any gas in which the cohesive forces between molecules are negligible and the collisions between molecules are perfectly elastic; that is, both momentum and kinetic energy are conserved. Many real gases behave as ideal gases at temperatures well above their boiling points and at low pressures.

The English scientist Robert Boyle, the 14th child of the Earl of Cork, was an infant prodigy. At the age of eight, he spoke Greek and Latin, and at 14, he traveled to Italy to study the works of Galileo. He returned to England in 1645 to find his father dead and himself wealthy. In 1654, he became a member of the “Invisible College,” which later became the Royal Society, where he met Newton, Halley, and Hooke.

In 1662, while experimenting with gases, he was able to show that if a fixed amount of a gas was kept at a constant temperature, the pressure and the volume of the gas follow a simple mathematical relationship. Boyle discovered that gases were compressible, so that when the pressure was increased (as when the piston in Figure 11.1a is pushed down by the extra sand), the volume of the gas decreased. Boyle further found that if the container was placed on a hot plate kept at a constant temperature, the increase in pressure was matched by the decrease in volume. This meant that if the pressure was doubled, the volume halved; if the pressure was tripled, the volume decreased to exactly one-third. Boyle expressed this relationship between pressure and volume as

PV = constant [at constant temperature].

This expression is known today as Boyle’s law. Several years after Boyle’s experiments, it was found that the constant in Boyle’s law was the same for all gases.

Throughout the eighteenth century, many scientists investigated the expansion of gases when heat was added, but their results lacked consistency and no conclusion regarding the dependence among volume, pressure, and temperature was reached. In 1804, the French chemist Joseph Louis Gay-Lussac was able to show that if the pressure of the gas was kept constant (as illustrated in Figure 11.1b with the constant weight of the sand on the frictionless lid), then the change in volume was proportional to the change in temperature. He investigated this relationship between temperature and volume with air, hydrogen, oxygen, nitrogen, nitrous oxide, ammonia, carbon dioxide, hydrogen chloride, and sulfur dioxide, and found that it held consistently.

FIGURE 11.1 (a) A container filled with a gas kept at the same temperature by placing it on a temperature-

controlled hot plate. The pressure is changed by adding sand on the movable piston. When the pressure is increased, the volume decreases, (b) A fixed amount of sand on top of the frictionless lid maintains the gas in the container at a constant pressure. Increasing the temperature of the gas increases its volume in a linear way.

Since the volume and the temperature of a gas at constant pressure are directly proportional, a plot of volume versus temperature for different gases should give us straight lines for each gas. Gay-Lussac found that if these lines were extrapolated, they all cross the temperature axis at exactly the same point (Figure 11.2a). This point is the absolute zero of temperature, О К or -273.16°C. This was the basis for the introduction of the absolute or Kelvin scale of temperature.

The absolute zero is the minimum temperature attainable because at this temperature the volume of the gas would be zero, as we can see in the graph of Figure 11.2b. A plot of volume versus absolute temperature for an ideal gas yields a straight line that passes through the origin, as shown in Figure 11.2b, since T in Kelvin is zero for V = 0. Therefore,

This is Gay-Lussac’s law, also known as Charles’ law, because the French physicist Jacques Alexandre Charles had independently made the same discovery a few years earlier but had failed to publish it.

FIGURE 11.2 (a) A plot of volume versus temperature for different gases yields straight lines. When extrapolated, these lines intersect the temperature axis at -273°C. (b) A plot of volume versus absolute temperature for an ideal gas is a straight line through the origin.

We can combine Boyle’s law and Gay-Lussac’s law into one single expression, which is known as the ideal gas law.

We can extract a third relationship from the ideal gas law. When the volume of the gas remains constant, the pressure is proportional to the temperature:

We should keep in mind that the temperature T in all the gas laws is in kelvins.

PHYSICS IN OUR WORLD: AUTOMOBILE ENGINES

The gasoline engine used in automobiles is a heat engine that generates the input heat from the combustion of gasoline inside the engine. For this reason, gasoline engines are called internal combustion engines.

An automobile’s gasoline engine consists of the cylinder head, the cylinder block, and the crankcase. The cylinder head has two sets of valves, intake and exhaust. When the intake valves are opened, a mixture of air and gasoline enters the cylinders. When the exhaust valves are open, the burned gases are expelled from the cylinders. The valves are opened and closed by the camshaft, a system of cams on a rotating shaft, while the moving pistons turn a shaft, the crankshaft, to which they are connected. The camshaft and the crankshaft are interconnected by a drive belt or chain so that as the pistons move, turning the crankshaft, the camshaft is also turned, opening and closing the valves.

Most automobiles have a four-stroke cycle engine. In the intake stroke, the downward motion of the piston draws fuel into the cylinder. The volume of the cylinder increases from a minimum volume Vmin to a maximum volume Vnm = rVmin, where r is the compression ratio. For modern automobiles, the compression ratio is between eight and ten. In the compression stroke, the intake valve closes as the piston reaches the end of the downstroke, and the piston compresses the air-fuel mixture to Vmhl. In the power stroke, an electric spark from the spark plug ignites the gases, increasing their temperature and pressure. The heated gases expand back to Етах, pushing the piston and doing work on the crankshaft. Finally, in the exhaust stroke, the exhaust valve opens, and the piston moves upward, pushing the burned gases out of the cylinder. The cylinder is now ready for the next cycle.