Specific heat capacity

• Specific heat capacity e.g:

  1kg of water at 25 Celsius -> Absorbs 4200J of heat energy -> 1kg of water at 26 Celsius.

  • The water remains liquid throughout the heating process.
• Specific heat capacity (SHC):


  The amount of heat energy (in joules) required to raise the temperature of 1 kg of a substance by 1 Celsius without changing its state.

  Also as the amount of energy released by a substance as it cools.

  • Unit: J/kg$^{\circ}$C
• Energy transfer (J) = mass (kg) x specific heat capacity (J/Kg℃) x Change in temperature (℃)
• E = m x C x Δθ
• • m = E / C x Δθ
  • C = E / m x Δθ
  • Δθ = E / m x C
  • Ε = mcΔθ
• Energy transfer per second, depends upon:

  • Type of substance (specific heat capacity)
  • Mass of substance
  • The amount of the substance
  • Temperature difference (final temp. - initial temp.)
• A block of copper metal with a mass of 1.3kg is heated from 25℃ to 45℃.

  • The specific heat capacity of copper is 380J/Kg℃.

  Calculate the energy needed to heat the copper to 45℃

  E = mcΔθ

  • m = 1.3Kg
  • c = 380J/Kg℃
  • Δθ = 45℃ - 25℃ = 20℃

  E = 1.3 x 380 x 20 = 9880J
• A can of drink is cooled from 20℃ to -5℃. The mass of the can of drink is 0.33kg. The specific heat capacity of the drink in can is 3900J/Kg℃.

  Calculate the energy transferred from the can to the surroundings.

  E = mcΔθ

  • m = 0.33kg
  • c = 3900J/Kg℃
  • Δθ = -5℃ - (-20℃) = -25℃

  E = 0.33 x 3900 x -25 = -32175J
• When the temperature of 0.25kg of ice cream is increased from -10℃ to -2℃, the heat supplied is 3000J.

  • Find the specific heat capacity of the ice cream.

  c = e $\div$ (m x Δθ)

  • e = 3000J
  • m = 0.25Kg
  • Δθ = -2℃ - (-10℃) = 8℃

  c = 3000 $\div$ (0.25 x 8) = 1500J/Kg℃
• Whenever you heat up or cool down an object.

  • there's a CHANGE IN ENERGY.
• Specific heat capacity (SHC):

  A property of a material that tells you how easy it is to HEAT UP or COOL DOWN.

  
• • Water takes 4186 Joules to heat 1 kg of water by 1°C.
  • Oil has a lower SPECIFIC HEAT CAPACITY of 1670 J/kg°C, so it needs LESS energy to heat up.

  Meaning the oil heats up and cools down more easily than water.

  
• Change in thermal energy (J) = Mass (Kg) x Specific Heat Capacity (J/Kg℃) x change in temperature (℃)

  • ΔΕ = mcΔθ
• 500g of oil with a specific heat capacity of 1670 J/kg℃ is heated from 25℃ to 42℃.

  • Calculate the amount of thermal energy transferred to the oil.

  ΔΕ = mcΔθ

  • Mass = 500g / 1000 = 0.5 Kg
  • SHC = 1670 J/kg℃
  • Change in temp. = 42℃ - 25℃ = 17℃

  Thermal energy = 0.5 x 1670 x 17 = 14.195 J
• Internal energy:


  The total energy stored by the particles making up a substance or system, it’s made up of:

  • Potential energy stores
  • Kinetic energy stores

  
• Potential energy stores:

  • Things like gravitational & elastic potential, but they’re not really related to temp.

  Kinetic energy stores:

  • The movement energy of the particles.

  
• • The particles in a solid have kinetic energy because they are vibrating.
  • The particles in a liquid or gas have kinetic energy because they move around.
• In physics:

  • Energy change is measured in joules
  • mass is measured in kilograms
• E = mcΔθ

  Δθ = E / mc

  • Δθ = 46200J $\div$ 0.5Kg x 4200J/Kg℃ = 22℃

  The temperature of the water in the kettle after 2 hrs:

  • 100℃ - 22℃ = 78℃