Final answer:
To find the specific heat of the metal, we use the principle of heat transfer, applying the formula “Q = mcΔT” to equate the heat lost by the metal to the heat gained by the water, allowing us to calculate the unknown specific heat value.
Step-by-step explanation:
The question asks to calculate the specific heat of a metal after it is placed in a calorimeter with water and both reach thermal equilibrium. We can use the principle of heat transfer, which states that the heat lost by the metal will be equal to the heat gained by the water. The formula to use is Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Firstly, we calculate the heat gained by the water using Q = mcΔT, where m is 20.00 ml of water (which is equivalent to 20.00 g, assuming the density of water is about 1 g/mL), c is the specific heat capacity of water (4.18 J/g°C), and ΔT is the change in temperature of water from 22.1 °C to 26.8 °C.
Then, we calculate the heat lost by the metal using the same formula, but we do not know the specific heat of the metal, so we write it as cmetal. Since the metal cools down from 48.6 °C to 26.8 °C, ΔT for the metal is negative.
Lastly, setting the heat gained by the water equal to the heat lost by the metal and rearranging the formula allows us to solve for cmetal, the specific heat of the metal.