A 375 g piece of iron was heated to 975 °C and then quenched in a bucket containing one gallon of water at 20 °C. What was the temperature of the water after the iron and the water came to thermal equilibrium?
Convert one gallone water to\] liters. Then liters x 1000 = mL and that, with the density of water = 1g/mL, will be grams water.
[mass water x specific heat water x (Tfinal-Tinitial)] + [mass Fe x specific heat Fe x (Tfinal-Tinitial)] = 0
Solve for Tfinal which is the only unknown in the equation.
To determine the final temperature of the water after it comes to thermal equilibrium with the iron, we can use the principle of energy conservation. The total heat lost by the iron will equal the total heat gained by the water.
First, let's calculate the heat lost by the iron using the formula:
Q = mcΔT
where:
Q is the heat lost by the iron
m is the mass of the iron (375 g)
c is the specific heat capacity of iron (0.449 J/g°C)
ΔT is the change in temperature of the iron (final temperature - initial temperature)
Since the initial temperature of the iron is not given, we'll assume it was at room temperature (20 °C), and the final temperature is known (975 °C). Therefore, ΔT = 975 °C - 20 °C = 955 °C.
Now, let's calculate the heat lost by the iron:
Q = (375 g) * (0.449 J/g°C) * (955 °C)
Next, let's calculate the heat gained by the water. We can use the same formula, but this time we'll consider the specific heat capacity of water (4.184 J/g°C) and the change in temperature as the final temperature of the water (which we need to find) minus the initial temperature of the water (20 °C):
Q = (1 gallon) * (3.78541 L/gallon) * (1000 g/L) * (4.184 J/g°C) * (final temperature - 20 °C)
Since the heat lost by the iron equals the heat gained by the water:
(375 g) * (0.449 J/g°C) * (955 °C) = (1 gallon) * (3.78541 L/gallon) * (1000 g/L) * (4.184 J/g°C) * (final temperature - 20 °C)
Solving the equation for the final temperature of the water will give us the answer.