A calorimeter at 15 °C contains 0.1 kg of carbon. The calorimeter is made of aluminium and its mass is 0.02 kg. When 892 J of heat is added to the calorimeter and carbon, the temperature increases to 28 °C. The specific heat capacity for aluminium is 900 J kg-¹ K-1. Find the specific heat capacity of carbon.
Question
A calorimeter at 15 °C contains 0.1 kg of carbon. The calorimeter is made of aluminium and its mass is 0.02 kg. When 892 J of heat is added to the calorimeter and carbon, the temperature increases to 28 °C. The specific heat capacity for aluminium is 900 J kg-¹ K-1. Find the specific heat capacity of carbon.
Solution
To find the specific heat capacity of carbon, we first need to calculate the amount of heat absorbed by the aluminium calorimeter and then subtract this from the total heat added to find the heat absorbed by the carbon.
Step 1: Calculate the heat absorbed by the aluminium calorimeter The formula for heat absorbed is Q = mcΔT, where m is mass, c is specific heat capacity, and ΔT is the change in temperature.
For the aluminium calorimeter: Q_aluminium = m_aluminium * c_aluminium * ΔT Q_aluminium = 0.02 kg * 900 J kg-¹ K-1 * (28°C - 15°C) Q_aluminium = 0.02 kg * 900 J kg-¹ K-1 * 13 K Q_aluminium = 234 J
Step 2: Calculate the heat absorbed by the carbon The total heat added to the system was 892 J, so the heat absorbed by the carbon is the total heat minus the heat absorbed by the aluminium.
Q_carbon = Q_total - Q_aluminium Q_carbon = 892 J - 234 J Q_carbon = 658 J
Step 3: Calculate the specific heat capacity of the carbon We can rearrange the formula for heat absorbed to find the specific heat capacity: c = Q / (mΔT).
For the carbon: c_carbon = Q_carbon / (m_carbon * ΔT) c_carbon = 658 J / (0.1 kg * 13 K) c_carbon = 505.38 J kg-¹ K-1
So, the specific heat capacity of carbon is approximately 505.38 J kg-¹ K-1.
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