Temperature and Internal Energy

FIELDS OF STUDY: Thermodynamics; Classical Mechanics

ABSTRACT: The temperature of an object or substance is actually the average thermal energy of all its particles. The standard unit for temperature is the kelvin (K). Thermal energy, like all forms of energy, is measured in joules (J). It is in fact a subtype of kinetic energy, based on the motion of the particles that make up matter.

PRINCIPAL TERMS

• enthalpy: a measure of the total internal energy (thermal energy) of a system, the product of its volume and pressure.
• heat: the active process of energy transfer due to changes in an object’s thermal energy.
• ideal gas law: a law stating that the pressure (P) and volume (V) of an ideal gas are directly related to its number of particles (n), its temperature (T), and the ideal gas constant (R).
• kinetic energy: the energy an object possesses due to its motion.
• potential energy: the energy stored within an object due to its position (e.g., gravitational pull on a stationary object above the ground) or its configuration (e.g., an electrical charge or chemical makeup).
• static energy: electrical energy resulting from an imbalance in electrical charges.
• temperature gradient: a measurement of the rate of temperature change over distance.
• thermal energy: energy generated by the movement of particles within an object or substance.

A Measure of Internal Energy

Temperature does not simply indicate how hot or cold a given object or substance is. An object’s temperature, measured in kelvins (K), degrees Celsius (°C), or degrees Fahrenheit (°F), is actually a measure of the average thermal energy contained in that object. The hotter the object, the higher its temperature and the more energy contained within. Thermodynamics is the branch of physics concerned with the study of thermal energy.

The language of thermodynamics can be confusing, as much of its terminology has general-use definitions as well. Specifically, temperature measures the average thermal energy contained in the particles of an object. Like all forms of energy, it is measured in joules (J). Recall that all matter, even solid materials, consists of molecules and atoms with lots of space between them. Even the carbon atoms in a diamond, locked into a crystalline structure of incredible hardness, constantly vibrate imperceptibly. Because thermal energy is generated by the movement of individual particles, it is closely related to kinetic energy. Indeed, thermal energy is sometimes called "thermal kinetic energy." However, "thermal energy" refers specifically to the average kinetic energy of the particles in an object, while "kinetic energy" refers to any energy associated with motion, whether of an entire object or of its individual molecules.

When the temperature of an object changes, the particles in it speed up or slow down accordingly. A temperature gradient describes the direction and rate of temperature change in terms of temperature per unit of distance. In International System of Units (SI) units, this is measured in kelvins per meter (K/m). Heat, in thermodynamics, is a process of energy transfer or loss, not a property of an object.

Common Temperature Scales

The three most common temperature scales are the Kelvin scale, the Celsius scale, and the Fahrenheit scale. The kelvin is the standard unit for scientific work, although Celsius is often used as well. The Kelvin scale is distinguished by the fact that 0 kelvin corresponds to absolute zero, the point at which all motion is thought to cease. Water freezes at 273 kelvins and boils at 373 kelvins. Celsius is based on the freezing and boiling points of water, set at 0 and 100 degrees Celsius, respectively. The Fahrenheit scale, used for everyday temperature readings in the United States, was developed based on the lowest temperature to which brine could be cooled and the average human body temperature. On the modern scale, pure water freezes at 32 degrees Fahrenheit and boils at 212 degrees Fahrenheit. Equations for converting between the temperature scales are below:

Conservation of Energy

The law of conservation of energy states that in an isolated system—one from which neither matter nor energy can escape—energy is conserved. The universe is, in theory, the ultimate isolated system. Therefore, according to this law, energy in the universe can be neither created nor destroyed, only transformed or transferred.

When a system loses thermal energy as heat, that energy is transformed into another form of energy. Often, heat is generated as a by-product when other forms of energy, such as static energy, are transferred. Resistance causes some static energy being transferred along wires to be transformed into thermal energy and lost to the surrounding environment as heat. Lightbulbs transform electrical energy into heat and light.

Energy can exist in a variety of forms, some of which cannot be directly observed. Potential energy is stored energy an object possesses due to its position or configuration. The chemical structure of food holds potential energy that is released by digestion. The body eventually turns a portion of this potential energy into the kinetic energy of moving limbs and beating hearts.

When the transfer of energy results in displacement, work has been done. Work, like energy, is measured in joules. Transferring one unit of energy is equivalent to performing one unit of work. Many devices use heat to perform work. The engine of a car uses heat from a spark plug to release the fuel’s chemical potential energy through combustion. This released energy increases the kinetic energy of the gas particles in the piston chamber. These particles bounce off the walls of the chamber with increasing force, pushing the piston. The pistons transmit their kinetic energy to the driveshaft, which transmits it to the wheels. Ultimately the wheels impart kinetic energy to the entire vehicle, producing forward motion. For the sake of study, an engine can be considered an isolated system, retaining all matter and energy within it. However, real-world factors such as refueling and exhaust emissions (input and output of matter) actually make it an open system.

Particles in Motion: The Ideal Gas Law

Gases are particularly illustrative when studying the relationship between temperature, thermal energy, kinetic energy, and particle motion in a substance. In a gas, the particles are free to bounce around. Therefore, a gas will expand to fill any container of any shape. In addition, gas particles are in constant motion, bouncing off the walls of the container as well as each other. This causes the gas to exert outward pressure on the container.

Heating a gas raises not only its temperature but also the pressure exerted on its container. This relationship is one of several laid out in the ideal gas law:

PV = nRT

This law describes the relationships between pressure (P), typically measured in kilopascals (kPa); volume (V), measured in cubic meters (m³); the number of particles (n), measured in moles (mol); and the temperature (T), measured in kelvins. It also includes the ideal gas constant (R), equal to approximately 8.314 J/mol·K.

The relationships to temperature can be better seen when the equation is rewritten as follows:

T = PV/nR

From this equation, it is clear that increasing either the pressure or the volume of a gas will raise its temperature. Conversely, increasing the number of particles will cause the temperature to drop. This makes intuitive sense, given the definition of temperature. Adding more particles will lower the average kinetic energy of each particle.

Although the particles of solids and liquids are more rigidly bound than those of gases, the same relationships hold for the other phases of matter. Increasing the pressure on ice, for instance, causes it to melt more quickly. A larger block of ice has more particles, so it takes longer to melt than a smaller block would under the same conditions.

The enthalpy (H) of a system is equal to its total internal (thermal) energy (U) plus the product of its volume and pressure. Only when the system’s overall energy changes can the enthalpy be measured. This is written as

∆H = ∆U + ∆PV

or

∆H = ∆U + P∆V

Temperature is directly related to enthalpy. When the temperature of a system rises, so too does its thermal energy, and thus so does its enthalpy.

Sample Problem

(A) An air temperature of 90 degrees Fahrenheit is considered quite hot. What is the equivalent temperature in Celsius, the scale used in European countries? What is it in kelvins, the standard unit of temperature?

(B) Absolute zero is 0 kelvin. What is the corresponding temperature in Celsius? What is it in Fahrenheit?

Answer:

To convert between temperature scales, use the equations above. Note that the math for converting to or from Fahrenheit is slightly more complicated due to the fact that the individual degrees are not the same size as degrees Celsius and kelvins.

(A) To convert from Fahrenheit to Celsius and to kelvins, use the following equations:

Simply plug in the Fahrenheit value given and solve:

Ninety degrees Fahrenheit is approximately equal to 32.22 degrees Celsius.

It is also approximately equal to 305.37 kelvins.

(B) To convert from kelvins to Celsius and to Fahrenheit, use the following equations:

°C = K − 273.15

°F = (K − 273.15)(1.8) + 32

Simply plug in the kelvin value given and solve:

°C = 0 K − 273.15

°C = −273.15

Zero kelvin is equal to −273.15 degrees Celsius.

°F = (0 K − 273.15)(1.8) + 32

°F = −491.67 + 32

°F = −459.67

It is also equal to −459.67 degrees Fahrenheit.

Temperature in the Everyday

Knowing the temperature of various objects and of the environment is immensely useful. Extremes of temperature in either direction can be dangerous, causing injuries or maladies such as burns, heatstroke, or frostbite. Understanding the various relationships that underpin thermodynamics is also helpful, albeit in more subtle ways. The ideal gas law explains why covering a pot causes it to boil faster (increased pressure raises temperature). Knowing that heat is often a by-product of other energy-transfer processes can help diagnose wiring problems in electronics when they seem to be running hotter than usual. It can even lead to a deeper understanding of human health. One major reason mammals eat (i.e., consume potential chemical energy) so often is to maintain a high internal body temperature. This benefits mammals’ disease resistance, metabolism, and homeostasis in both hot and cold environments.

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