5.1.6 Specific Heat Capacity

• The specific heat capacity of a substance is defined as:

The amount of thermal energy required to raise the temperature of 1 kg of a substance by 1 °C

• This quantity determines the amount of energy needed to change the temperature of a substance
• The specific heat capacity is measured in units of Joules per kilogram per Kelvin (J kg^-1 K^-1) or Joules per kilogram per degree Celsius (J kg^-1 °C^-1) and has the symbol c
  • Different substances have different specific heat capacities
  • Specific heat capacity is mainly used when considering liquids and solids

• From the definition of specific heat capacity, it follows that:
  • The greater the mass of the material, the more thermal energy that will be required to raise its temperature
  • The greater the change in temperature, the higher the thermal energy required to achieve this change

Low v high specific heat capacity

• If a substance has a low specific heat capacity, it heats up and cools down quickly
• If a substance has a high specific heat capacity, it heats up and cools down slowly
• The specific heat capacity of different substances determines how useful they would be for a specific purpose eg. choosing the best material for kitchen appliances

Table of values of specific heat capacity for various substances

• Good electrical conductors, such as copper and lead, have low specific heat capacities
  • This makes them excellent conductors of heat
  • It is due to their free electrons

• The amount of thermal energy Q needed to raise the temperature by Δθ for a mass m with specific heat capacity c is equal to:

E = mcΔθ

• Where:
  • E = change in thermal energy (J)
  • m = mass of the substance (kg)
  • c = specific heat capacity of the substance (J kg⁻¹K⁻¹ or J kg⁻¹ °C⁻¹)
  • Δθ = change in temperature (K or °C)

Step 1: State the known quantities

• • Power = 1.7 kW = 1.7 × 10³ W
  • Time = 3.5 minutes = 3.5 × 60 s = 210 s
  • Mass, m = 650 g = 0.65 kg
  • Temperature change, Δθ = 100 − 25 = 75 °C           

Step 2: State the equation linking energy, power and time

Energy = Power × Time

Step 3: Calculate the energy supplied

Energy = 1.7 × 10³ × 210 = 3.57 × 10⁵ J

Step 4: State the thermal energy equation

E = mcΔθ

Step 5: Rearrange to make specific heat capacity the subject

Step 6: Substitute in values and state the final answer

 J kg⁻¹ °C⁻¹

• In these experiments the following equation is used to determine the specific heat capacity of the substance:

Methods to Determine the Specific Heat Capacity of a Solid and a Liquid

Equipment List for a Solid:

• A block of the substance (preferably 1kg in mass)
• A thermometer
• An appropriate heater (e.g., an immersion heater)
• A power source
• A joule meter or a voltmeter, ammeter and stop-clock

 

Apparatus to determine the specific heat capacity of a 1 kg Aluminium block

Method for a Solid

1. Assemble the apparatus as shown in the diagram above
2. Measure the initial temperature of the substance
   • Record the value
3. Turn on the power supply and start the stop-clock
4. Take readings of the voltage and current
   • Record these values
5. After 5 minutes (300 seconds) switch off the power supply, stop the stop-clock
6. Monitor the thermometer
   • Record the highest temperature reached
   • This may be a few minutes after the power supply is switched off

Equipment List for a Liquid:

• A beaker of liquid (ideally containing 400 ml liquid)
• A thermometer
• An appropriate heater (e.g., an immersion heater)
• A power source
• A joule meter or a voltmeter, ammeter and stop-clock
• A digital balance

Apparatus to determine the specific heat capacity of 400 ml of water 

Method for a Liquid

1. Assemble the apparatus as shown in the diagram above
2. Measure the mass of the liquid 
   • Record the value
3. Measure the initial temperature of the substance
   • Record the value
4. Turn on the power supply and start the stop-clock
5. Take readings of the voltage and current
   • Record these values
6. After 10 minutes (600 seconds) switch off the power supply, stop the stop-clock
7. Monitor the thermometer
   • Record the highest temperature reached
   • This may be a few minutes after the power supply is switched off

Analysis of the Results

• Calculate the change in temperature
  • This is the final temperature minus the initial temperature
• The heat supplied to the substance can be calculated using the equation:

energy = current (A) × voltage (V) × time (s)

• The equation for specific heat capacity can be used to calculate specific heat capacity

E = mcΔθ

• Where:
  • E = change in thermal energy (J)
  • m = mass of the substance (kg)
  • c = specific heat capacity of the substance (J kg⁻¹K⁻¹ or J kg⁻¹ °C⁻¹)
  • Δθ = change in temperature (K or °C)

Evaluation

• Not all of the heat supplied by the heater will go into the substance
  • Some heat will be lost to the surroundings 
  • This means that the value for energy supplied will be too large
  • This results in too high a value for specific heat capacity
• There may be fluctuations in the power supply
  • Take several periodic measurements of the voltage and current
  • Calculate an average of these values