when it absorbed energy from a 79.4 g sample of water whose initial temperature was 70.1 °C. What is the specific heat of the metal in J/g·°C?
How do i get the final temperature of water
To find the final temperature of water, you can use the principle of heat transfer, which states that the heat gained by the water is equal to the heat lost by the metal:
Heat gained by water = Heat lost by metal
The heat gained by the water can be calculated using the equation Q = m * c * ΔT, where Q is the heat gained (in joules), m is the mass of water (in grams), c is the specific heat capacity of water (4.18 J/g·°C), and ΔT is the change in temperature.
Given:
Mass of water (m) = 79.4 g
Initial temperature of water = 70.1 °C
Final temperature of water (unknown)
Specific heat capacity of water (c) = 4.18 J/g·°C
Let's assume the final temperature of water is T.
Using the equation Q = m * c * ΔT for water, we can rewrite it as:
Q_water = (m_water) * (c_water) * (T - initial temperature)
Now, since the heat gained by the water is equal to the heat lost by the metal:
Q_water = Q_metal
The heat gained by the water is also equal to the heat lost by the metal, which can be calculated using the equation Q = m * c * ΔT for the metal. However, we need to rearrange the equation to solve for ΔT:
ΔT_metal = Q_metal / (m_metal * c_metal)
Now, we have the initial temperature, the final temperature of water (T), and we can assume the final temperature of the metal is the same as the initial temperature of the water. Plug in the values into the equation and solve for the unknown:
ΔT_metal = (m_water * c_water * (T - initial temperature)) / (m_metal * c_metal)
Plug in the known values:
ΔT_metal = (79.4 g * 4.18 J/g·°C * (T - 70.1 °C)) / (m_metal * c_metal)
Simplify the equation further and solve for the specific heat capacity of the metal (c_metal):
c_metal = (79.4 g * 4.18 J/g·°C * (T - 70.1 °C)) / (m_metal * ΔT_metal)
By rearranging the equation and plugging in the known values, you can calculate the specific heat capacity of the metal in J/g·°C.