# Specific Heat Capacity(OCR A Level Physics)

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Katie M

Expertise

Physics

## 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

## Determining Specific Heat Capacity

• 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−1K1 or J kg1 °C1)
• Δθ = change in temperature (K or °C)

#### Worked example

A kettle has a power rating of 1.7 kW. A mass of 650 g of liquid at 25 °C is poured into the kettle.

When the kettle is switched on, it takes 3.5 minutes to start boiling.

Calculate the specific heat capacity of the liquid.

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 kg1 °C1

#### Exam Tip

The difference in temperature Δθ will be exactly the same whether the temperature is given in Celsius or Kelvin. Therefore, there is no need to convert between the two since the difference in temperature will be the same for both units.

## Procedures to Determine Specific Heat Capacity

• 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−1K1 or J kg1 °C1)
• 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

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