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)
Oops, sorry. Posted a second time by accident.
Right. I did this for you yesterday.
To solve this problem, we can use the principles of heat transfer and the specific heat capacities of tin and water. The formula for heat transfer is:
Q = m * C * ΔT
Where:
Q is the heat transfer
m is the mass
C is the specific heat capacity
ΔT is the change in temperature
In this case, we have two heat transfers happening:
1. The heat transfer from the heated tin to the water.
2. The heat transfer within the water to raise its temperature.
Let's find the heat transfer from the tin to the water first using the formula above.
Q1 = m1 * C1 * ΔT1
Where:
Q1 is the heat transfer from the tin to the water
m1 is the mass of the tin
C1 is the specific heat capacity of tin
ΔT1 is the change in temperature of the tin
We know that the initial temperature of the tin is 695 °C, and the final temperature of the system is 30.7 °C. So:
ΔT1 = (30.7 °C - 695 °C) = -664.3 °C
Substituting the given specific heat capacity of tin (C1 = 0.227 J/g°C), the mass of the tin (m1), and the change in temperature (ΔT1) into the equation, we can solve for Q1.
Now, let's find the heat transfer within the water using the same formula:
Q2 = m2 * C2 * ΔT2
Where:
Q2 is the heat transfer within the water
m2 is the mass of the water
C2 is the specific heat capacity of water
ΔT2 is the change in temperature of the water
We know that the initial temperature of the water is 23.2 °C, and the final temperature of the system is 30.7 °C. So:
ΔT2 = (30.7 °C - 23.2 °C) = 7.5 °C
Substituting the given specific heat capacity of water (C2 = 4.18 J/g°C), the mass of the water (m2 = 158 g), and the change in temperature (ΔT2) into the equation, we can solve for Q2.
Finally, we can equate Q1 and Q2 since they are part of the same system:
Q1 = Q2
m1 * C1 * ΔT1 = m2 * C2 * ΔT2
Now, we can rearrange the equation to solve for the mass of the tin dropped into the water (m1):
m1 = (m2 * C2 * ΔT2) / (C1 * ΔT1)
Substituting the given values into the equation will give us the mass of the tin dropped into the water.