0625 · 2.2Thermal properties and temperature

Particles, internal energy and temperature

0:00A bridge needs room to expand on a hot day. Water can keep boiling without becoming hotter. Sweat can cool your skin even when the surrounding air feels warm. These situations share one explanation, which is that energy changes the motion and arrangement of particles. By the end, you will understand thermal expansion, specific heat capacity, and changes of state. We need a short reminder of the particle model. Solids contain closely packed particles that vibrate about fixed positions.

0:26Liquid particles are close together but can move past one another. Gas particles are widely separated and move freely. These different arrangements help explain why materials respond differently when their temperature rises. Internal energy is the total energy of the particles inside an object. It includes their kinetic energy from movement and their potential energy associated with their arrangement. A rise in an object’s temperature increases its internal energy. However, an object can also gain internal energy without its temperature rising, as we will see during melting and boiling.

0:57Here is our first Supplement idea for Extended students. An increase in temperature means an increase in the average kinetic energies of all the particles in the object. Individual particles do not all have the same energy. Temperature describes an average, rather than the energy of every particle separately.

Thermal expansion in solids, liquids and gases

1:13Let us begin with thermal expansion. Most materials expand when their temperature rises and contract when it falls. Expansion means an increase in dimensions, such as length or volume. We are describing expansion at constant pressure. The material must be able to expand rather than being completely confined inside a rigid container. The particle explanation is Supplement content. In a heated solid, particles vibrate more vigorously about their fixed positions.

1:39Their average separation usually increases slightly, so the solid expands. The particles themselves do not become bigger. It is the increased spacing between particles that makes the whole object larger. In a liquid, particles also gain kinetic energy as the temperature rises. They move more vigorously, and their average separation generally increases. Their arrangement is less constrained than the arrangement in a solid. For comparable temperature increases, liquids generally expand more than solids, although the amount depends on the substance.

2:09A gas shows the greatest expansion. Heating makes its particles move faster, so they collide more vigorously with the walls and a movable piston. The piston moves outwards until the gas pressure again matches the external pressure. The same gas particles now occupy a larger volume, with greater average separation between them. Compare equal starting volumes given the same temperature rise at constant pressure. Gases generally expand much more than liquids, and liquids generally expand more than solids.

2:36Solid and liquid particles remain close together because of attractive forces. Gas particles are much farther apart, so the gas can undergo a much larger increase in volume. Bridge expansion gaps allow the deck to become longer without pushing dangerously against neighbouring sections. Long metal pipes also need arrangements that accommodate expansion. A tight metal jar lid can sometimes be loosened by warming it briefly. The metal lid expands, helping it move more easily around the cooler glass beneath.

3:02A liquid thermometer uses expansion deliberately. As its liquid warms, the liquid expands more than the surrounding glass. The extra volume moves up the narrow tube, producing a visible change in level. Another application is a bimetallic strip, made from two bonded metals that expand by different amounts. Heating bends the strip, allowing it to operate a switch. Two ideas must be kept separate. Expansion is a change in size.

3:26A temperature rise is an increase in the average kinetic energy of the particles. Neither of these tells us directly how much energy was supplied. Different materials need different amounts of energy for the same temperature rise, even when their masses are equal.

Specific heat capacity calculations

3:39This next section is Supplement content for Extended students. Specific heat capacity is the energy required per unit mass per unit temperature increase. Its unit is joules per kilogram per degree Celsius. A high specific heat capacity means that a material needs more energy to produce a given temperature rise. Imagine heating two equal masses with equal energy inputs. If one material has a higher specific heat capacity, its temperature rises less.

4:05This does not mean that it receives less energy. Instead, more energy is needed for each degree of temperature increase. Specific heat capacity connects energy input, mass, and temperature change. Specific heat capacity equals change in energy divided by mass multiplied by change in temperature. The denominator means the product of mass and temperature change. Rearranging gives change in energy equals mass multiplied by specific heat capacity multiplied by temperature change.

4:32Twice the mass needs twice the energy for the same rise. For a first worked example, suppose a metal block has a mass of zero point five zero kilograms. It receives twelve thousand joules of energy. Its temperature rises from twenty degrees Celsius to fifty degrees Celsius. We will calculate its specific heat capacity, assuming that all the supplied energy heats the block. First, subtract twenty from fifty to find a temperature change of thirty degrees Celsius.

4:57Next, multiply zero point five zero kilograms by thirty degrees Celsius to obtain fifteen kilogram degrees Celsius. Then divide twelve thousand joules by fifteen kilogram degrees Celsius. The specific heat capacity is eight hundred joules per kilogram per degree Celsius. Notice that we used the temperature change, not the final temperature. Specific heat capacity describes the energy needed to raise temperature, so the increase is what matters. We also used mass in kilograms.

5:24Using five hundred grams directly in this calculation would give the wrong numerical answer for the stated unit. For our second calculation, consider zero point two five kilograms of water. Its specific heat capacity is given as four thousand two hundred joules per kilogram per degree Celsius. We want its temperature to rise by twenty degrees Celsius. This time, we know the material property and need to calculate the required energy.

5:49First, use energy equals mass multiplied by specific heat capacity multiplied by temperature change. Multiply zero point two five by four thousand two hundred to obtain one thousand and fifty. Then multiply one thousand and fifty by twenty. The required energy is twenty-one thousand joules, assuming no energy is transferred to the surroundings.

Measuring specific heat capacity

6:08We can measure a solid’s specific heat capacity using a metal block, an electric heater, and a thermometer. First, measure the block’s mass and record its initial temperature. Place the heater and thermometer in suitable holes in the block. Good thermal contact helps energy enter the block and makes the temperature reading more representative. Wrap the block in insulation to reduce energy transfer to the surroundings. Supply a measured energy input, using a joulemeter, and record the final temperature.

6:34Calculate the temperature rise, then divide the supplied energy by mass multiplied by temperature rise. Repeat the measurement to check consistency, keeping the temperature rise moderate to limit energy losses. The energy measured by the joulemeter is not necessarily all absorbed by the block. Some warms the apparatus, and some escapes to the surroundings. If we count all that energy as heating the block, the calculated specific heat capacity is too high.

6:58Insulation reduces this problem but does not eliminate it completely. For a liquid, measure the empty container’s mass and then its mass with the liquid inside. Subtract to obtain the liquid’s mass, and record its initial temperature. Immerse the heater and thermometer, then supply a measured amount of energy. Stir gently so that the liquid’s temperature is reasonably uniform throughout. Use insulation and a lid to reduce energy losses, without sealing the container airtight.

7:24Record the final temperature and calculate the temperature increase. Apply the same specific heat capacity equation as before. Some supplied energy warms the container, so an accurate measurement must allow for this as well as energy transferred to the surroundings.

Changes of state and evaporation

7:38So far, energy input has produced a temperature rise. During a change of state, the situation is different. At standard atmospheric pressure, pure water melts at zero degrees Celsius and boils at one hundred degrees Celsius. While melting or boiling occurs at constant pressure, energy is supplied without a change in temperature. Imagine heating ice that begins below its melting temperature. Its temperature rises until it reaches zero degrees Celsius.

8:03During melting, the temperature remains constant while solid ice becomes liquid water. Once all the ice has melted, further energy input raises the water’s temperature towards its boiling temperature. At one hundred degrees Celsius, boiling begins at standard atmospheric pressure. Energy continues entering, but the temperature remains constant while liquid water changes into water vapour. A flat section on the heating graph does not mean energy input has stopped. It means the supplied energy is producing a change of state rather than a temperature rise.

8:32The energy changes the arrangement of particles by overcoming attractive forces between them. During melting, particles become able to move past one another. During boiling, particles separate much farther apart to form a gas. Their average kinetic energy does not increase during these constant-temperature changes, although their internal energy increases. Cooling can reverse these changes. In condensation, gas particles lose energy and come closer together as a liquid forms. In solidification, a liquid becomes a solid as particles become arranged around fixed positions.

9:03They still vibrate, but they no longer move freely past one another. These changes transfer energy from the substance to its surroundings. Condensation does not mean particles disappear, and solidification does not mean particles stop moving completely. Water vapour condensing on a cold window becomes liquid droplets. Liquid water solidifying becomes ice. For pure water at standard atmospheric pressure, solidification occurs at zero degrees Celsius. This is the same temperature as melting.

9:32Evaporation is another way for a liquid to become a gas. Some particles have more energy than others, even when the liquid has a single measured temperature. More-energetic particles at the surface can escape from the liquid. Evaporation therefore happens at the surface and can occur below the boiling temperature. Evaporation causes cooling because the escaping particles carry energy away. After more-energetic particles leave, the average kinetic energy of the remaining particles decreases.

9:57Since temperature is linked to average kinetic energy, the liquid’s temperature falls unless energy is supplied to replace the loss. This explains why an evaporating liquid can cool. The detailed comparison between boiling and evaporation is Supplement content. Boiling occurs throughout a liquid, with vapour bubbles forming inside it. It occurs at the boiling temperature for the existing pressure. Evaporation occurs only at the surface and can happen at any temperature at which the substance is liquid.

10:24Three factors affect evaporation rate, also part of the Supplement. A higher temperature means a greater proportion of particles have enough energy to escape. A larger surface area exposes more particles at the surface. These changes increase the number of particles escaping each second, so evaporation happens faster. Air movement also increases evaporation. Moving air carries water vapour away from the region just above the liquid. This reduces the return of vapour particles to the liquid and allows faster net evaporation.

10:54That is why spreading wet clothes out and placing them in moving air helps them dry. Supplement students must also explain cooling of an object in contact with an evaporating liquid. Sweat provides a familiar example. Evaporation removes energy from the liquid on your skin. Energy is transferred from your skin to the liquid, reducing your skin’s internal energy and temperature. Sweat cools effectively when it evaporates, not merely because it is present.

Exam explanations and recap

11:17Let us apply this to an exam-style task. Explain why water in a shallow dish evaporates faster when a fan blows across it. Focus on what the moving air changes above the surface. Do not claim that the fan must heat the water, because increased air movement can increase evaporation without raising its temperature. A suitable answer is this. Moving air carries water vapour away from above the liquid surface.

11:40Fewer vapour particles return to the liquid, so net evaporation increases. More-energetic particles escape and carry energy away. The average kinetic energy of the remaining liquid particles decreases, so the liquid cools unless that energy is replaced. Another exam task might ask you to explain a horizontal section on a heating graph. State that the substance is melting or boiling, depending on the section shown. Energy is supplied to overcome attractive forces and change the particle arrangement.

12:08Average particle kinetic energy remains constant, so the temperature does not rise. Keep the main misconceptions separate. Heating does not always raise temperature, because energy can cause a change of state. When a material expands, its particles do not grow larger but move farther apart. Evaporation is not boiling, because it happens only at the surface. Specific heat capacity is a material property, not the total energy stored in an object.

12:32Let us finish with the central idea. Energy can increase average particle kinetic energy, producing a temperature rise, or change particle arrangement during a change of state. Thermal expansion generally results from increased average separation. Specific heat capacity tells us the energy required per unit mass per unit temperature increase. Evaporation removes more-energetic particles and can cool both a liquid and an object touching it.