IBDP Physics : Topic 3. Thermal physics-3.1 Thermal concepts : study Notes

THERMAL PROPERTIES OF MATTER

TEMPERATURE

• Lower fixed point (LFP) is the freezing point of water.
• Upper fixed point (UFP) is the boiling point of water.

IDEAL GAS EQUATION

• Boyle’s law : When temperature is held constant, the pressure is inversely proportional to volume.

i.e., ( at constant temperature)

• Charle’s law : When the pressure is held constant, the volume of the gas is directly proportional to the absolute temperature.

i.e., (at constant pressure)

• Avogadro’s law :  When the pressure and temperature are kept constant, the volume is directly proportional to the number of moles of the ideal gas in the container.

i.e., (at constant pressure and temperature)

ABSOLUTE TEMPERATURE

1. 1. The mercury thermometer with cylindrical bulb are more sensitive than those with spherical bulb.
   2. Alcohol thermometer is preferred to the mercury thermometer due to the larger value of the coefficient of cubical expansion.
   3. Properties that make mercury the ideal thermometric substance are :
      1. It does not stick to the glass walls
      2. Available in pure form
      3. Low thermal conductivity and low specific heat
      4. Vapour Pressure is low
      5. Coefficient of expansion is uniform
      6. It shines
   4. Gas thermometer is more sensitive than the mercury thermometer, because its coefficient of cubical expansion is much larger.
   5. At the following temperatures different temperature scales have the same reading :
      1. Fahrenheit and Reaumur at –25.6ºF = –25.6ºR
      2. Reaumur and Celsius at 0ºR = OºC
      3. Celsius and Fahrenheit at –40ºC = –40ºF
      4. Fahrenheit and Kelvin at 574.25ºF = 574.25K
   6. The Celsius scale and the Kelvin cannot have the same reading at any temperature.
   7. Six’s thermometer measures minimum and maximum temperature during a day. It uses mercury as well as alcohol as the thermometric substances.
   8. Normal human body temperature is 37ºC = 98.6ºF.
   9. Clinical thermometers are much shorter than the laboratory thermometers because they are used to measure a limited range (96º F to 100º F) of temperature.
   10. Rapidly changing temperature is measured by using thermo electric thermometer.
   11. The temperature inside a motor engine is measured using platinum resistance thermometer.
   12. The radiation thermometers can measure temperature from a distance.
   13. Adiabatic demagnetisation can be used to measure temperature very near to the absolute zero.
   14. The Rankine is the smallest temperature range among all the scales of temperature.
   15. When a substance is heated it expands along each dimension in the same proportion. (if it is uniform)

THERMAL EXPANSION

THERMAL EXPANSION OF SUBSTANCES

or      

where β = coefficient of area expansion

where γ = coefficient of volume expansion. The units of α, β and γ is (°C)–1 or K–1.

1. 1. During change in temperature, the mass does not change but the density decreases due to increase in volume. Therefore
      
   2. Relation between α, β and γ

and

1. 3. Water has negative coefficient of volume expansion for temperature range (0°C – 4°C). Therefore water contracts when the temperature rises from 0°C to 4°C and then expands as the temperature increases further.

THERMAL EXPANSION OF LIQUID (WHICH IS HEATED IN A VESSEL)

where    = apparent change in volume

if , but
if , is positive and the liquid rises in the vessel and
if , is negative and liquid falls in vessel.

CHANGE IN DENSITY OF SOLIDS AND LIQUIDS WITH TEMPERATURE

THERMAL STRESS

Thermal stress =  

EFFECT OF TEMPERATURE  ON PENDULUM CLOCK

 …..(i)

We have

 …..(ii)

 

(since  is very small)

Loss of time per day
( ⸪ no. of seconds in one day = 86400 sec.)

ERROR IN SCALE READING

ISOTHERMAL AND ADIABATIC ELASTICITIES

• Isothermal elasticity  
  (since PV = RT = constant, )
• Adiabatic elasticity

;   where

EXPANSION OF GASES

• Pressure coefficient of expansion of gas (γP)

where P0 = Pressure at 0°C,  Pt = Pressure at t°C

• Volume coefficient of expansion of gas (γv)

where V0 = Volume at 0°C, Vt = Volume at t°C

HEAT

• Calorie : It is the amount of heat required to raise the temperature of 1g of water from 14.5ºC to 15.5ºC.

• Kilocalorie, 1 Kcal = 1000 cal
• British Thermal Unit (BTU) : It is the fps unit of heat = 252 cal = amount of heat required to raise the temperature of 1 lb of water through 1ºF (from 63°F to 64ºF).

SPECIFIC HEAT CAPACITY

Specific heat capacity,

• Molar specific heat at constant volume (CV) : It is the amount of heat required to raise the temperature of 1 mole of a gas through 1K or 1°C at constant volume.

• Molar specific heat at constant pressure (CP) : It is the amount of heat required to raise the temperature of 1 mole of a gas through 1K or 1°C at constant pressure.

THERMAL CAPACITY OR HEAT CAPACITY

WATER EQUIVALENT

PRINCIPLE OF HEAT (OR CALORIMETRY)

LATENT HEAT

• Latent heat of fusion : It is the quantity of heat required to change unit mass of the solid into liquid at its melting point.

• Latent heat of vaporisation : It is the quantity of heat required to convert unit mass of liquid  into vapour at its boiling point.

DIFFERENT PROCESSES OF PHASE CHANGE OR STATE CHANGE

• Sublimation : It is the process of conversion of solids to gaseous state on heating. On cooling the vapours get converted back into solids.
• Condensation : It is the process of conversion of gases/vapours to liquid state on cooling. On heating, these liquids are converted into vapours/gases.
• Boiling : It is the process of conversion of liquid to gaseous state on heating. It is a cooling process.
• Melting : It is the process in which solid gets converted into liquid on heating.
• Evaporation : Conversion of liquid into gaseous state at all temperatures is called evaporation. It is a phenomenon that occurs at the surface of the liquid.

1. 1. The heat capacity or thermal capacity depends on nature of the substance (specific heat capacity) and mass of quantity of matter of the body.
   2. In case of melting and boiling, the temperature does not change, only intermolecular potential energy of the system changes.
   3. System are in thermal equilibrium when their temperature are same or average kinetic energy per molecule is same.
   4. Internal energy is the sum of all energies in a system which includes energy of translational, rotational as well as vibrational motion of the molecules.
   5. The molar specific heat capacity depends on the molecular weight of the substance.
   6. The temperature, volume or pressure of a system may remain constant when it absorbs heat.
   7. When we press two block of ice together such that after releasing the pressure two block join this phenomenon is called regelation.

PHASE DIAGRAM

• The diagram shows vaporisation curve (AB), fusion curve (CD), sublimation curve (EF).
• For water, AB is called steam line, CD is called ice line and EF is called hoar-frost line.
• The temperature at which all the three states of matter (solid, liquid, gas) are mutually in thermal equilibrium is called the triple point (point P in diagram) of the substance.
• The temperature upto which a gas can be liquified under pressure alone is called the critical temperature (Tc).

SATURATED AND UNSATURATED AIR

VAPOUR PRESSURE

HUMIDITY

i.e.,

i.e.,

1. 1. Hygrometry is the branch of thermal physics that deals with the measurement of amount of water vapours present in the atmosphere.
   2. Hygrometer is an instrument used to determine dew point and relative humidity.
   3. Relative humidity is low when the air is dry.
   4. Saturated vapours do not obey (except Dalton’s law) gas laws, while unsaturated vapours obey them. The S.V.P. varies linearly with temperature (keeping volume constant) and equal to one atmospheric pressure at boiling point.(shown in fig.(a)) S.V.P. constant at constant temperature on increasing or decreasing volume fig. (b).

   

1. 5. At 0ºC, the saturation vapour pressure is 4.6 mm of Hg. Therefore, water vapours are always present around the ice. It increases with the increase in temperature.
   6. The relative humidity is 100% when the temperature of the atmosphere is equal to the dew point.
   7. Cryogenics is the study of low temperature.
   8. As RH is expressed in percentage, hence the maximum value of RH may be 100%.
   9. The saturation vapour pressure of water at 100ºC is 760 mm of Hg at sea level.
   10. As the temperature rises, the absolute humidity may increase and the relative humidity may remain constant or may even decrease.
   11. If the relative humidity is high then at the same temperature one feels hotter.
   12. If the air is absolutely dry, the dew point is not observed.
   13. The relative humidity decreases with the increase in temperature.
   14. If water is sprinkled in the room, both relative humidity as well as the dew point increase.
   15. Dew appears on the leaves of the trees etc. due to the condensation of saturated vapours.
   16. The mist or fog is the small droplets of water formed due to the condensation of water vapours near the surface of earth.
   17. Mist or fog formed much higher above the surface of earth is called cloud.
   18. The Relative humidity between 50% and 60% gives comfortable feeling to human beings.
   19. When the relative humidity is 100%, the reading of the dry and wet bulbs is same.
   20. Smaller the difference in the temperature of dry and wet bulbs, larger is the relative humidity.
   21. Water vapours are always seen around the ice, because the temperature around it is less than the dew point.

HEAT TRANSFER

• Conduction
• Convection
• Radiation

CONDUCTION

The rate of heat flow as found experimentally is given by

where

⇒  …(1)

CONVECTION

RADIATION

1. 1. The equation is valid for steady state condition. The condition is said to occur when no part of heat is used up in raising the temperature of any part of cross-section of the solid.
   2. On comparing equation (1) with the following equation used for flowing of charge on account of potential difference.

We find :

The role of resistance (thermal resistance) is played by

1. 3. Series combination of conductors

 

1. 4. Parallel combination of conductors

Keq =

1. 5. Davy’s safety lamp is based on the conduction. It is used in mines to know the ignition temperature of gases. Danger of explosion can be avoided.
   6. Principle of chimney used in a kitchen or a factory is based on the convection.
   7. Land and sea breezes are due to the convection.
   8. Temperature of the upper part of the flame is more than the temperature on the sides, because the currents of air carry the heat upwards.
   9. Radiation can be detected by differential air thermometer, Bolometer, thermopile, etc.

HEAT TRANSFER BY RADIATION AND NEWTON’S LAW OF COOLING

STEFAN’S LAW

for perfectly black body ….(1)

 ….(4)

 ….(5)

and   ….(6)

WIEN’S LAW

    

Hence on increasing temperature of a body, its colour changes gradually from red orange yellow green  blue violet. Thus the temperature of violet star is maximum and temperature of red star is minimum. Sun is a medium category star with λm = 4753Aº (yellow colour) and temperature 6000K.

KIRCHOFF’S LAW

i.e. 

• For a perfect black body, A = 1,
  
• If emissive and absorptive power are considered for a particular wavelength λ then
• Since Eλ is constant at a given temperature, according to this law if a surface is good absorber of a particular wavelength then it is also a good emitter of that wavelength.

FRAUNHOFER’S LINE

• Fraunhofer lines are the dark lines in the spectrum of sun and are explained on the basis of Kirchoff’s law. When white light emitted from central core of sun (photosphere) passes through its atmosphere (chromosphere) radiation of those wavelength will be absorbed by the gases present there, which they usually emit (as good emitter is a good absorber) resulting dark lines in the spectrum of sun.
• On the basis of Kirchoff’s law, Fraunhofer identified some of the elements present in the chromosphere. They are hydrogen, helium, sodium, iron, calcium, etc. Fraunhofer had observed about 600 darklines in the spectrum of sun.

NEWTON’S LAW OF COOLING

i.e.    

and where, e = emissivity of body, A = area of surface of body, σ = Stefan’s constant, m = mass of body, c = specific heat of body.

SOLAR CONSTANT

• Good absorber is a good emitter.
• Cooking utensils are provided with wooden or ebonite handles, since wood or ebonite is a bad conductor of heat.
• Good conductor of heat are good conductors of electricity, Mica is an exception which being a good conductor of heat is a bad conductor of electricity.