A piece of copper weighing 400g is heated to 100C and then quickly transferred to a copper calorimeter of mass 10g containing 100g of liquid of unknown specific heat capacity at 30C. If the final temperature of mixture is 50C, calculate the specific heat capacity of the liquid. (Specific heat capacity of copper = 390J/Kg/K
First, we need to calculate the heat lost by the copper and the heat gained by the liquid in order to determine the specific heat capacity of the liquid.
Heat lost by copper = Heat gained by liquid
\(m_1c_1\Delta T_1 = m_2c_2\Delta T_2\)
Where:
- \(m_1\) = mass of copper = 400g = 0.4kg
- \(c_1\) = specific heat capacity of copper = 390J/kg/K
- \(\Delta T_1\) = change in temperature of copper = (50°C - 100°C) = -50°C
- \(m_2\) = mass of liquid = 100g = 0.1kg
- \(c_2\) = specific heat capacity of liquid (unknown)
- \(\Delta T_2\) = change in temperature of liquid = (50°C - 30°C) = 20°C
Substitute the values into the equation:
\(0.4kg * 390J/kg/K * -50°C = 0.1kg * c_2 * 20°C\)
\(-78J = 2 * c_2\)
\(c_2 = -39J/Kg/K\)
Since specific heat capacity can't be negative, this means there was an error in the calculation. Let's review the equation and try again.