Heat Transfer: Thermodynamics and Specific Heat

• This chapter explores how to determine the amount of heat a substance loses or gains during heating, cooling, or phase changes.
• This chapter includes the study of the specific heat of materials and methods of measuring it, as well as the first law of thermodynamics and its applications.

Heat and Its Effects

• Raising a substance's temperature requires supplying it with heat energy.
• Lowering a substance's temperature requires removing heat energy.
• The amount of energy needed to heat or cool a substance depends on:
  • Mass of the substance.
  • Magnitude of the temperature change.
  • Specific heat of the substance.
• During boiling, melting, and sublimation, materials absorb heat without changing temperature.
• During condensation and freezing, materials release heat while maintaining a constant temperature.
• Studying heating, cooling, boiling, melting, condensation, sublimation, and freezing reveals:
  • Energy supplied to a substance increases the kinetic or vibrational energy of its atoms or molecules, raising its temperature. The opposite is also true to a point. The substance retains its state, whether solid, liquid, or gas.
  • Absorbing or releasing heat during boiling, melting, sublimation, condensation, and freezing does not change the substance's temperature; instead, the energy is used to alter or break the bonds between atoms or molecules. The reverse happens when these bonds form.

Heat Quantity (Q)

• Energy conservation can determine the amount of heat (Q) a substance gains or loses using the following relationship:
  • Heat Lost = Heat Gained
• Important points to consider when estimating the amount of heat lost or gained by a substance:

  • First Case: Change in Substance Temperature

    • During heating or cooling, the amount of heat (Q) gained or lost in ONLY raising or lowering the temperature is given by:
      • Q = m * C * ΔT
        • m is the mass, C is the specific heat, and ΔT is the temperature change.

  • Second Case: Change in State of Substance

    • Using Q = mL, the heat (Q) needed for materials to change state (boiling, melting, sublimation, freezing, condensation) without changing their temperature can be expressed as:
      • L represents the latent heat of fusion, vaporization, or sublimation.

  • Third Case: Change in Nature or Composition of Substance

    • This includes magnetic or electrical changes, or changes in the composition of the material, that occur when the temperature of the material changes.

Mechanical Equivalent of Heat (J)

• Heat is a form of energy measured in calories or kilocalories.
• Converting heat into mechanical work and vice versa is possible.
• The conversion factor between heat energy and mechanical energy is called the mechanical equivalent of heat (J) with the following relationship:
  • W = JQ
    • Mechanical energy can convert into heat energy and vice versa.
    • Best estimates are as follows:
      • 1 calorie equals 4.186 Joules
      • 1 Kilocalorie equals 4186 Joules

Specific Heat of Materials (C)

• Specific heat capacity is the amount of heat needed to change the temperature of a unit mass of a substance by one degree.
• It is denoted by C and expressed mathematically as:
  • C = ΔQ / (m * ΔT)
    • ΔQ represents the amount of heat supplied to a mass m, causing its temperature to change by ΔT.
    • Specific heat is measured in J/Kg.K, J/g.K, J/mole.K, or cal/g.K.
• The specific heat of a substance greatly depends on temperature.
  • Stating temperature when giving specific heat values is essential.
  • Water's specific heat at room temperature is approximately 4.2 x 10^3 J/Kg.K.
• The heat capacity and specific heat of all materials decrease as temperature decreases, reaching zero at absolute zero.
• Heat capacity is the amount of heat needed to raise the temperature of a substance by one degree, measured in J/K.
• The heat capacity of a material relates to its specific heat as:
  • Heat Capacity = Mass x Specific Heat
• The following relationship can determine the quantity of heat (Q) given to a body of mass m and specific heat C to raise its temperature from T1 to T2 :

Measuring Specific Heat

• Numerous methods can measure specific heat; these differ based on the range of low or high temperatures.

Electrical Method for Measuring the Specific Heat of Solid Materials

• Used for solids that conduct heat well (e.g., copper, aluminum).
• A regularly shaped piece of the material with a hole which holds a heater (electric component) and a sensor (thermometer).
• The mass of the material and its initial temperature are measured, then the metal piece is surrounded by insulating material (wool, polystyrene).
• An electric current (I) is passed through the heater for a measured time.
• The voltmeter (V) and ammeter (I) readings and the time are recorded.
• After a period of time, the current is stopped and the highest temperature reached is recorded using the thermometer.
• The assumption is the heat dissipated from the metal to the environment is zero, then,
  • Electrical energy provided by the heater equals the heat provided to the metal piece
    • m * C * (T2 – T1 ) = V * I * t
    • So, re-arranging C = VIt / (m (T2 - T1))

Electrical Method for Measuring the Specific Heat of Liquid Materials

• This method is similar to the one for solids.
• A calorimeter is used to hold the liquid and contains an electrical heater and a sensor, the liquid being stirred.
• The mass of the liquid (m), mass of the calorimeter (me), initial temperature (T1), and final temperature (T2), Voltmeter reading (V), Ammeter reading (I) and the time are recorded. - The heat capacity of the calorimeter and stirrer must be known. - The following formula may be used: - Energy supplied by the heater = Energy gained by theliquid + Energy gained by the calorimeter and the stirrer - mC (T₂ – T₁ ) = V I t - mC｡(T2 – T₁)

Mixing Method to Find Specific Heat of Solid Materials

• The solid material undergoes a procedure to evaluate its specific heat using this method: - Determine the mass of the material required to find the specific heat. - It must be attached to a string and be put in boiling water. - Leave for ten minutes allowing for its temperature to become the equivalent T3 = 100 degrees Celcius. - Quickly transfer to a calorimeter of mass (m.) containing a mass of water (mw). - Ensure the temperatures of the liquid are recorded to T1. - Measure the final temperature on the calorimeter (T2) and calculate the specific heat capacity. - It is important that the heat is recorded, and a suitable known quantity is taken.
  • Assuming that the solid does not lose heat during the transfer to the calorimeter:
    • Heat gained to calorimeter + heat gained to water = heat lost to solid

Mixing Method to Find Specific Heat of Liquid Materials

• It is close to Method 3, where a solid with a known heat value is selected.
• The equations used previously are used to find the thermal capacity of the liquid.
• Other methods can measure the specific heat of materials, such as the continuous flow method, the mechanical method, and the cooling method.

Triple Point of a Substance

• Changes in a substance's state upon temperature change can be affected by applied pressure.
• The boiling point of water increases with pressure until it reaches a critical value.
• This means that a substance will not stay in a liquid state regardless, with any pressure applied above a point.
• The pressure at which boiling changes with temperature is named curve of boiling.
• Solid melting points are dependent on pressure.
• Thawing has pressure applied but thawing under pressure makes something bend.
• The melting of ice is called the curve of melting.
• The melting temperature of ice lowers with increased pressure, as well as melts against any bodies.
• Changing the temperature for any other solid and high pressure gives increases in temperature.
• Sublimation follows two key methods which support pressure.
• These aspects can be taken advantage of, one being on ice since a certain amount of pressure induces sliding and can come about with a certain slope.
• An alternate factor that supports skiing is the slope under certain turns.
• It is a factor that aids in sliding or bending since a certain amount of pressure induces a sliding effect.

States of Matter Transitions

• Processes where the state of matter changes are called phase changes.
• Phase changes happen with melting of metal, and the liquids change with boiling into a gas (steam).
• Phase changes in steam occur in endothermic stages.
• Heat is added to the matter, however, there is no associated temperature reading.
• Internal energy is for matter only, with changes being more direct when transferring from liquid to the next phase.
• Water has phases, where solid ice is less than steam liquid form.
• Alternative phase changes come about internally and transition to their physicals aspects through electricity or a new design.
• These phases of transition happen as with temperatures, and in particular are a phase of heat as with vaporization that happen in states like the boiling and or melting points.

Evaporation

• Latent heat of evaporation can be defined as heat which can result in a combination of liquid parts with the gas phase but fixed with pressures.
• Heat is removed as the gas turns back to fluid form with phases fixed to heat.
• Latent heat varies to temperature, there is less linking with steam temperature with liquid amounts and phases.
• Most latent heat is what helps overcome bonds within the liquid, and also helps in the procedure to support certain compression from the force in some liquids, as is the case in pressure within storms in the heat.
• Heat measurements follow different forms, which are dependent on measurements of kilo and Joules.
• When some fluid goes into a container without air with the compounds then moving into air, a little compound comes back into some liquid, moving through processes of change.
• Under some given condition, pressures are linked and do not adjust for things and measurements.
• Vapors exist beneath circumstances through pressure, and liquids in said areas move high or low through conditions and certain pressures.

Melting

• Heat in melting or fusion helps a material combine a solid, to a liquid at a heat.
• These points of heat are given in tables, as energy helps in a liquid state, thus energy helps make items in great condition.
• Heat is measured and used to treat connections as with components in great order.

Boiling

• Gases need portions of fluids to remove to exist.
• Steam relies on the fluid heat and stress. Heat is taken from the fluid in a boiling situation.
• Liquids that steam have great value and power and strength.

Sublimation

• A subject will no stay a set gas under a number in three components, as pressures and amounts.

First Law

• A gas that goes to heat is a volume level and may have more stress.
• Stress in phases can change through conditions to volume phases and or temperatures as phases can occur.
• A set amount of compressed wind and heat requires great power to start and manage.
• The power and heat between elements is written as the quantity of change.