College Physics - Chapter 14: Heat and Heat Transfer Methods

Heat and Heat Transfer Methods

Introduction to Heat

  • Heat transfer occurs due to temperature differences between objects or systems.
  • Heat is defined as energy that is transferred solely because of a temperature difference.
  • When objects with different temperatures interact (e.g., a soft drink and ice), energy is transferred until they reach thermal equilibrium at the same temperature (T').

Mechanical Equivalent of Heat

  • It's possible to alter a substance's temperature by performing work on it.
  • This demonstrates that heat is a form of energy.
  • James Prescott Joule's experiments established the mechanical equivalent of heat, which relates work to heat transfer.
  • 1.00 \text{ kcal} = 4186 \text{ J}

Heat Transfer and Temperature Change

  • The amount of heat transferred is directly proportional to the temperature change.
    • Doubling the temperature change requires twice the heat.
  • The amount of heat transferred is directly proportional to the mass.
    • Doubling the mass requires twice the heat for an equivalent temperature change.
  • The amount of heat transferred depends on the substance and its phase.
    • Different substances require different amounts of heat to achieve the same temperature change.

Factors Affecting Heat Transfer

  • Transferred heat (Q) depends on:
    • Change in temperature (\Delta T)
    • Mass of the system (m)
    • Substance and its phase
  • Equation for heat transfer: Q = mc\Delta T
    • Q = heat transfer
    • m = mass
    • \Delta T = change in temperature
    • c = specific heat (depends on the material and phase)
  • SI unit for specific heat: J/(kg·K) or J/(kg·°C)
  • Specific heat is the amount of heat needed to change the temperature of 1.00 kg of a substance by 1.00 °C.

Example: Heating Water in an Aluminum Pan

  • A 0.500 kg aluminum pan is used to heat 0.250 kg of water from 20.0 °C to 80.0 °C.
  • Specific heat of water: 4186 J/kg·°C
  • Specific heat of aluminum: 900 J/kg·°C
  • The pan and water are at the same temperature.
  • When the pan is heated, both the pan and water experience the same temperature increase.

Phase Change and Latent Heat

  • During a phase change (e.g., ice melting), no temperature change occurs despite heat transfer.
  • Most substances exist in solid, liquid, or gas phases.
  • Phase changes occur at fixed temperatures for a given substance and pressure (boiling and freezing/melting points).
  • Heat absorbed or released during phase changes is given by:
    • Q = mL_f (melting/freezing)
    • Q = mL_v (vaporization/condensation)
    • L_f = latent heat of fusion
    • L_v = latent heat of vaporization

Example: Chilling Soda with ice cubes

  • Three ice cubes at 0 °C are used to chill 0.25 kg of soda at 20 °C.
  • Each ice cube has a mass of 6.0 g.
  • The soda is in a foam container to minimize heat loss.
  • Assume the soda has the same heat capacity as water (4186 J/kg·°C).
  • Latent heat of fusion of water: 334 kJ/kg
  • Melting of ice occurs in two steps: phase change (ice to water at 0°C), then temperature increase of the water.

Heat Transfer Methods

  • Heat is transferred by conduction, convection, and radiation.
  • In a fireplace, radiation is primarily responsible for heat transfer.
  • Conduction occurs at a slower rate.
  • Convection occurs through air movement (cold air entering, hot air leaving).

Conduction

  • Conduction is heat transfer between objects in direct contact.
  • Example: Heat transferring to your hands when holding a hot cup of coffee.
  • The rate of conductive heat transfer is given by: \frac{Q}{t} = kA\frac{(T2 - T1)}{d}
    • \frac{Q}{t} = rate of heat transfer (energy per unit time)
    • d = thickness or distance between objects
    • A = contact area
    • k = thermal conductivity
    • T2 - T1 = temperature difference

Example: Ice Box

  • A styrofoam ice box has a total area of 0.950 m² and walls with an average thickness of 2.50 cm.
  • The box contains ice, water, and canned beverages at 0 °C.
  • The outside temperature is 35 °C.
  • Thermal conductivity of styrofoam: 0.010 J/s·m·°C
  • Latent heat of fusion of water: 334 kJ/kg

Convection

  • Convection is heat transfer by the macroscopic movement of mass.
  • Convection can be natural or forced and is generally faster than conduction.
  • Example: Steaming milk for hot cocoa.

Radiation

  • Radiation is heat transfer through the emission or absorption of electromagnetic waves.
  • Example: Reheating coffee in a microwave.
  • The rate of heat transfer by radiation is determined by the Stefan-Boltzmann law: \frac{Q}{t} = \sigma eAT^4
    • \frac{Q}{t} = rate of heat transfer (energy per unit time)
    • \sigma = Stefan-Boltzmann constant (5.67 x 10-8 J/s·m²·K⁴)
    • e = emissivity of the body (0 to 1)
    • A = surface area
    • T = temperature in Kelvin
  • The net rate of heat transfer by radiation is related to both the object's temperature and its surroundings' temperature:
    • \frac{Q{net}}{t} = \sigma eA(T1^4 - T_2^4)

Example: Radiation from a Person

  • An unclothed person is standing in a dark room with an ambient temperature of 22.0 °C.
  • The person's skin temperature is 33.0 °C, and the surface area is 1.50 m².
  • The emissivity of skin is 0.97.
  • Stefan-Boltzmann constant: 5.67 x 10-8 J/s·m²·K⁴
  • T_2 = 22°C + 273 = 295 K
  • T_1 = 33°C + 273 = 306 K
  • \frac{Q}{t} = (5.67 × 10^{-8} J/s m^2 K^4)(0.97)(1.50 m^2)((306K)^4 - (295K)^4) = - 99 J/s = -99 W