A hot metal spoon with a mass of 77.0 grams and a temperature of 95.0 degrees celsius is placed into a cup containing 100 grams of water at 20 degrees celsius. When the spoon and water reach equilibrium, they both have a temperature of 25 degrees celsius. What is the spoon made of?
Copper
To determine what the spoon is made of, we need to use the principle of heat transfer known as heat capacity. The heat capacity of an object measures the amount of heat required to raise its temperature by a certain amount.
In this case, we know that the hot spoon and the water eventually reach equilibrium at a temperature of 25 degrees Celsius. This means that the heat lost by the spoon is equal to the heat gained by the water.
To calculate the heat lost by the spoon, we can use the formula:
q = m * c * ΔT
Where:
q is the heat lost by the spoon
m is the mass of the spoon
c is the specific heat capacity of the spoon material
ΔT is the change in temperature
First, let's calculate the heat lost by the spoon:
q_spoon = m_spoon * c_spoon * ΔT_spoon
q_spoon = 77.0 g * c_spoon * (95.0 °C - 25.0 °C)
Next, let's calculate the heat gained by the water using the same formula:
q_water = m_water * c_water * ΔT_water
q_water = 100 g * c_water * (25.0 °C - 20.0 °C)
Since the two quantities are equal (q_spoon = q_water), we can set them equal to each other and solve for c_spoon:
77.0 g * c_spoon * (95.0 °C - 25.0 °C) = 100 g * c_water * (25.0 °C - 20.0 °C)
Simplifying the equation gives:
c_spoon = (100 g * c_water * (25.0 °C - 20.0 °C)) / (77.0 g * (95.0 °C - 25.0 °C))
Now, we can substitute the known values:
c_spoon = (100 g * 4.18 J/g°C * (25.0 °C - 20.0 °C)) / (77.0 g * (95.0 °C - 25.0 °C))
After performing the calculations, we find:
c_spoon ≈ 0.39 J/g°C
This value corresponds to the specific heat capacity of the material the spoon is made of. By comparing this value to known specific heat capacities of different substances, we can determine what the spoon is made of.