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PHYSICS, M3 EQ-Bank 14

A student performs an experiment to determine the specific heat capacity of aluminium.

She heats a 0.40 kg block of aluminium to 90\(^{\circ}\)C, then quickly places it into a beaker containing 0.60 kg of oil at an initial temperature of 25\(^{\circ}\)C. After some time, the final equilibrium temperature of the aluminium and the oil is found to be 32\(^{\circ}\)C. The student knows that the specific heat capacity of the oil is 2.00 \(\times\) 10\(^3\) J kg\(^{-1}\)\(^{\circ}\)C\(^{-1}\).

Use this data to calculate the specific heat capacity of aluminium.   (4 marks)

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\(362\ \text{J/kg}^{\circ}\text{C}\)

Show Worked Solution
  • The energy lost by the block of aluminium is gained by the oil.
  •    \(Q_{\text{oil}} = mc \Delta T = 0.60 \times 2.00 \times 10^3 \times (32-25) = 8400\ \text{J}\).
  •    \(c_{\text{Al}} = \dfrac{Q}{m\Delta t} = \dfrac{8400}{0.4 \times (90-32)} = 362\ \text{J/kg}^{\circ}\text{C}\)
  • The specific heat capacity of Aluminium is \(362\ \text{J/kg}^{\circ}\text{C}\).

PHYSICS, M3 EQ-Bank 12

Define specific heat capacity and explain what it tells us about a substance.   (3 marks)

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  • Specific heat capacity is the amount of heat energy needed to raise the temperature of 1 unit of mass (usually 1 gram or 1 kilogram) of a substance by 1°C or 1 K.
  • It shows how easily a material’s temperature changes when heat is added or removed. Substances like water, with high specific heat capacity, absorb lots of heat with little temperature change.
  • Materials with low specific heat capacity heat up or cool down quickly, storing less thermal energy.
Show Worked Solution
  • Specific heat capacity is the amount of heat energy needed to raise the temperature of 1 unit of mass (usually 1 gram or 1 kilogram) of a substance by 1°C or 1 K.
  • It shows how easily a material’s temperature changes when heat is added or removed. Substances like water, with high specific heat capacity, absorb lots of heat with little temperature change.
  • Materials with low specific heat capacity heat up or cool down quickly, storing less thermal energy.

PHYSICS, M3 EQ-Bank 5

A 50 gram copper ball is placed into an insulated container containing 50 mL of water and immediately sealed. The initial temperature of the metal ball and water is 50°C and 10°C respectively. 

A student hypothesises that since the water and copper ball both have the same mass, the temperature of the metal ball and water, once thermal equilibrium is established, would be 30°C.

When the student measured the temperature inside the container, it was 26°C.

Explain the results of the experiment and why the student's hypothesis is incorrect.   (4 marks)

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  • Although the masses of the copper ball and water are the same, the specific heat capacities of the objects are different which leads to different changes in temperature.
  • The student’s hypothesis is incorrect as they did not take the specific heat capacity values into account.
  • The specific heat capacity of water is greater than that of copper, thus a greater amount of energy would be required to heat water to a certain temperature than to heat copper to that same temperature.
  • Therefore, when reaching a state of thermal equilibrium, the energy transfer between the copper ball and water cools the copper ball down faster than the water heats up.
  • This leads to the final temperature within the container of 26°C, which is closer to the initial temperature of the water than the copper ball.
Show Worked Solution
  • Although the masses of the copper ball and water are the same, the specific heat capacities of the objects are different which leads to different changes in temperature.
  • The student’s hypothesis is incorrect as they did not take the specific heat capacity values into account.
  • The specific heat capacity of water is greater than that of copper, thus a greater amount of energy would be required to heat water to a certain temperature than to heat copper to that same temperature.
  • Therefore, when reaching a state of thermal equilibrium, the energy transfer between the copper ball and water cools the copper ball down faster than the water heats up.
  • This leads to the final temperature within the container of 26°C, which is closer to the initial temperature of the water than the copper ball.