A one pound piece of iron was heated to 1000 °C

and then quenched in a bucket containing one gallon
of water at 25 °C. What was the temperature of the
water after the iron and the water came to thermal
equilibrium? correct answer is 37C

heat lost by Fe + heat gained by water = 0

[mass Fe x specific heat Fe x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Solve for Tf.

To find the temperature of the water after it came to thermal equilibrium with the iron, we can utilize the concept of heat transfer. The heat transferred from the hot iron to the cold water can be calculated using the equation:

Q = mcΔT

Where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.

Let's start by calculating the heat transferred from the iron to the water:

1. Calculate the heat transferred from the iron:
Q_iron = m_iron * c_iron * ΔT_iron

The mass of the iron is given as one pound, which is approximately 0.45 kilograms. The specific heat capacity of iron is about 0.45 Joules per gram per degree Celsius.

Converting the mass to grams:
m_iron = 0.45 kg * 1000 g/kg = 450 g

Substituting the values into the formula:
Q_iron = 450 g * 0.45 J/g°C * (1000 °C - 25 °C)

2. Calculate the heat transferred to the water:
Q_water = m_water * c_water * ΔT_water

The mass of the water is given as one gallon, which is approximately 3.78 liters or 3780 grams. The specific heat capacity of water is approximately 4.18 Joules per gram per degree Celsius.

Substituting the values into the formula:
Q_water = 3780 g * 4.18 J/g°C * (T_eq - 25 °C)

3. Since the heat transferred from the iron to the water is equal to the heat transferred to the water, we can set both equations equal to each other and solve for T_eq:

Q_iron = Q_water
450 g * 0.45 J/g°C * (1000 °C - 25 °C) = 3780 g * 4.18 J/g°C * (T_eq - 25 °C)

Simplifying the equation:
0.45 * 975 * 450 = 4.18 * 3780 * (T_eq - 25)
1962.75 = 15,854.04 * (T_eq - 25)
1962.75 = 15,854.04 * T_eq - 15,854.04 * 25
1962.75 + 15,854.04 * 25 = 15,854.04 * T_eq
39,956.75 = 15,854.04 * T_eq
T_eq = 39,956.75 / 15,854.04

Calculating the value:
T_eq ≈ 37 °C

So, the temperature of the water after coming to thermal equilibrium with the iron is approximately 37 °C.