A piece of tin is heated to 695 °C and dropped into 158 g of water at 23.2 °C. The temperature of the system rises to 30.7 °C. What is the mass of the tin dropped into the water?
(C = 0.227 J/g°C for tin, C = 4.18 J/g°C for water)
heat lost by Sn + heat gained by H2O = 0
[mass Sn x specific heat Sn x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for mass Sn. Post your work if you get stuck.
The mass of Sn would be 29.8 g?
Mass of tin is 32.8g
To solve this problem, we can use the principle of heat transfer:
The heat lost by the tin will be equal to the heat gained by the water.
Let's break down the steps to find the mass of the tin:
Step 1: Calculate the heat lost by the tin.
- Heat lost by tin = mass of tin x specific heat capacity of tin x change in temperature of tin
- The initial temperature of the tin is 695 °C.
- The final temperature of the tin is the same as the water's final temperature, which is 30.7 °C.
Step 2: Calculate the heat gained by the water.
- Heat gained by water = mass of water x specific heat capacity of water x change in temperature of water
- The initial temperature of the water is 23.2 °C.
- The final temperature of the water is 30.7 °C.
- The specific heat capacity of water is given as 4.18 J/g°C.
Step 3: Equate the heat lost by the tin to the heat gained by the water and solve for the mass of the tin.
Let's plug in the values and solve the equation:
Heat lost by the tin = Heat gained by the water
(mass of tin) x (specific heat capacity of tin) x (change in temperature of tin) = (mass of water) x (specific heat capacity of water) x (change in temperature of water)
(mass of tin) x (0.227 J/g°C) x (695 °C - 30.7 °C) = (158 g) x (4.18 J/g°C) x (30.7 °C - 23.2 °C)
Now we can solve for the mass of the tin:
(mass of tin) x (0.227 J/g°C) x (664.3 °C) = (158 g) x (4.18 J/g°C) x (7.5 °C)
mass of tin = [(158 g) x (4.18 J/g°C) x (7.5 °C)] / [(0.227 J/g°C) x (664.3 °C)]
mass of tin ≈ 114.38 g
So, the mass of the tin dropped into the water is approximately 114.38 g.