A piece of metal of mass 15 g at 119 ◦C is
placed in a calorimeter containing 48.8 g of
water at 23◦C. The final temperature of the
mixture is 58.9◦C. What is the specific heat
capacity of the metal? Assume that there is
no energy lost to the surroundings.
[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Plug in all the numbers given and solve for specific heat metal.
Post your work if you get stuck.
To find the specific heat capacity of the metal, we can use the principle of energy conservation.
The amount of heat gained by the metal can be calculated using the formula:
Qmetal = (mass of metal) * (specific heat capacity of metal) * (change in temperature)
The amount of heat lost by the water can be calculated using the formula:
Qwater = (mass of water) * (specific heat capacity of water) * (change in temperature)
Since there is no energy lost to the surroundings, the heat gained by the metal is equal to the heat lost by the water. Thus, we have:
Qmetal = Qwater
Now let's plug in the given values and solve for the specific heat capacity of the metal.
Mass of metal = 15 g
Specific heat capacity of metal = ?
Initial temperature of metal = 119 °C
Final temperature of mixture = 58.9 °C
Mass of water = 48.8 g
Specific heat capacity of water = 4.18 J/g°C (this is a commonly used value for water)
Initial temperature of water = 23 °C
Change in temperature (metal) = Final temperature - Initial temperature = 58.9 °C - 119 °C = -60.1 °C (Note: the negative sign is used because the metal is losing heat)
Change in temperature (water) = Final temperature - Initial temperature = 58.9 °C - 23 °C = 35.9 °C
Now we can set up the equation:
(mass of metal) * (specific heat capacity of metal) * (change in temperature metal) = (mass of water) * (specific heat capacity of water) * (change in temperature water)
(15 g) * (specific heat capacity of metal) * (-60.1 °C) = (48.8 g) * (4.18 J/g°C) * (35.9 °C)
Now, rearrange the equation to solve for the specific heat capacity of the metal:
(specific heat capacity of metal) = [(48.8 g) * (4.18 J/g°C) * (35.9 °C)] / [(15 g) * (-60.1 °C)]
Calculate the numeric value:
(specific heat capacity of metal) = 9.00 J/g°C
Therefore, the specific heat capacity of the metal is 9.00 J/g°C.