Heat Measurements

Units and Measured Quantities

• Thermal Energy: total potential and kinetic energy due to random motion and arrangement of molecules of the material
• Heat: thermal energy that is absorbed, given up, or transferred from one body to another
• Temperature: directly related to average kinetic energy of molecules, determines direction of heat flow between bodies
• Amount of thermal energy determines temp., but same amount of thermal energy will give different temp. in different substances
• Rumford & Joule showed heat is energy, not caloric fluid
• To be called heat, energy must be moving: a body may contain thermal energy, but not heat

Temperature Scales

• Fundamental unit of temp is the Kelvin

• Fahrenheit scale based on sea water: water freezes at 32 deg., boils at 212 deg.
• Celsius scale based on water: water freezes at 0 deg. boils at 100 deg.
• Kelvin scale zero point derived from temp. where ideal gas would have zero volume
• 0 K is called absolute zero, ~ -273.15 ^o C
• even at 0 K, matter has some energy and molecules still have some motion
• Kelvin scale now based on triple point of water, where all three phases are in equilibrium, 273.16 K or 0.01 ^o C
• Kelvin units are same size as Celsius degrees so K = ^o C + 273
• No negative temps in Kelvin scale
• Thermometer measures temperature using liquid (Hg or alcohol) or metal that expands linearly over useful temp. range

Heat Units

• Heat is difficult to measure, so usually measured by temp change produced

• Original unit of heat is the calorie, the heat needed to raise the temp of 1 g of water 1^o C
• The Calorie (with a capital C) is used to measure energy in food: equals 1 kilocalorie
• 1 calorie = 4.186 joules

Thermal Expansion

• Almost all substances expand when heated

• For solids, change in length per unit length for a certain temp change gives the coefficient of linear expansion, a
• Can be used to calculate length change by equation Dl = alDt
• Also have coefficients for area and volume expansion
• Liquids expand increasing volume and volume coefficient (B) is used: DV = BVDT

Expansion of Gases

• Gases also expand, use gas laws to calculate; assume constant quantity of dry, ideal gas

• Charles' Law (pressure constant): volume is directly prop. to Kelvin temp: V/ T = V'/ T'
• Boyle's Law (temp constant): volume is inversely proportional to pressure: pV = p'V'
• Combined gas law: pV/ T = p'V'/ T'
• If quantity of gas is allowed to change, universal gas law must be used: pV = nRT
• R is universal gas constant, 8.21 x 10^-2 L atm/mol K

Heat Transfer Mechanisms

• Conduction: energy transferred through molecular collisions; requires physical contact between objects

• Example: handle of frying pan
• Convection: in fluids, warmer areas expand, become less dense and rise creating convection currents
• Example: campfire, candle, weather
• Radiation: as electrons in energized atoms drop to lower energy levels, they emit radiation as electromagnetic waves (infrared); energy is absorbed by nearby objects completing heat transfer
• Examples: the sun, heat lamps, space heaters

Heat Exchange

• Heat capacity relates quantity of heat absorbed to temp change produced

• Specific heat ( c) is heat capacity per unit mass or amount of heat ( Q) needed to raise 1 g of the substance 1^o C
• To find heat needed to create temp change, use Q = mcDT
• When objects of different temps come into contact, hot object loses heat to cool object until both are at same temp.
• Heat lost = heat gained
• Heat exchange experiments conducted in insulated vessel called calorimeter which must be included in the calculations

Change of Phase

• Phase of pure substance is determined by temperature and pressure

• By changing temperature and/or pressure, phase change can be induced
• Temperature-pressure equilibrium graph can predict phase change (p. 188)
• Graph lines show boundaries between phases

Freezing and Melting

• Since liquid phase has higher potential energy than solid phase, heat must be added to melt a substance.

• Amount of heat needed to melt one gram of a substance at its melting point is called heat of fusion, L_F
• Heat of fusion for water (ice) = 334 J/g or 80 cal/g
• Temp will not rise until all of substance is melted: during melting, heat added changes potential energy, not kinetic energy.
• When liquid freezes, same amount of energy is released
• In heat exchange problems where melting or freezing occurs, heat required or released must be calculated using heat of fusion
• Since freezing releases energy, it is a warming process for the surroundings
• Since melting requires energy input, it is a cooling process for the surroundings
• Water can sometimes be supercooled below zero if very pure and motionless or moving very rapidly

Vaporization and Condensation

• At constant pressure, heat must be added to liquids to cause boiling or vaporization

• Amount of heat needed to vaporize 1 g of a liquid is its heat of vaporization, L_V
• L_V for water = 2260 J/g or 540 cal/g
• While substance boils, its temp remains constant; added energy increases potential energy of molecules creating phase change
• Evaporation, boiling, and sublimation are cooling process since heat is absorbed
• During condensation, heat of vaporization is released, so it is a warming process; steam burns are worse than hot water burns
• High pressure can condense gases as long as they are below a critical temperature above which they can't be liquefied at any pressure

Special Qualities of Water

• Water has very high specific heat; causes moderate climates in coastal regions; important for water cooled engines, hot water heating systems, cooking
• H₂O expands when cooled from 4 ^oC to 0 ^oC as ice structure begins to form; expands more when it freezes; H₂O is most dense at 4 ^oC; important for life in lakes, ponds, etc.