A 210 g iron bar is heated and then placed in 100. g of water in an insulated container. The water temperature increases from 21.2 °C to 53.3 °C. What was the initial temperature of the iron bar?

(Specific heats: cFe = 0.449 J/gK; cwater = 4.184 J/gK)

heat lost by Fe + heat gained by H2O = 0

[mass Fe x specific heat Fe x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial) = 0
Substitute and solve for Tinitial for Fe.

How much energy is required to heat 120.0g of water from 2.0°c to 24.0°c (Cp of H2O=4.184J/g

To solve this problem, we can use the concept of heat transfer and assume that there is no heat lost to the surroundings.

Let's break down the problem into steps:
1. Calculate the heat gained by the water.
2. Calculate the heat lost by the iron bar.
3. Equate the two amounts of heat to find the initial temperature of the iron bar.

Step 1: Calculate the heat gained by the water.
The formula to calculate heat (Q) is:
Q = m * c * ΔT

Where:
Q is the heat gained/lost (in joules)
m is the mass (in grams)
c is the specific heat capacity (in J/gK)
ΔT is the change in temperature (in °C or K)

Given:
m_water = 100 g
c_water = 4.184 J/gK
ΔT_water = 53.3 °C - 21.2 °C = 32.1 °C

Q_water = m_water * c_water * ΔT_water

Substituting the given values:
Q_water = 100 g * 4.184 J/gK * 32.1 °C

Step 2: Calculate the heat lost by the iron bar.
The heat lost by the iron bar will be equal to the heat gained by the water.

Q_iron = Q_water

Step 3: Equate the two amounts of heat to find the initial temperature of the iron bar.
The formula to calculate heat (Q_iron) is:
Q_iron = m_iron * c_iron * ΔT_iron

Where:
m_iron is the mass of the iron bar (in grams)
c_iron is the specific heat capacity of iron (in J/gK)
ΔT_iron is the change in temperature of the iron bar (initial temperature minus final temperature in °C or K)

Substituting the values:
Q_water = Q_iron
m_water * c_water * ΔT_water = m_iron * c_iron * ΔT_iron

Given:
m_iron = 210 g
c_iron = 0.449 J/gK

Substituting the given values:
100 g * 4.184 J/gK * 32.1 °C = 210 g * 0.449 J/gK * ΔT_iron

Now, solve for ΔT_iron:
(100 g * 4.184 J/gK * 32.1 °C) / (210 g * 0.449 J/gK) = ΔT_iron

Once you calculate ΔT_iron, subtract it from the final temperature of the iron bar to find the initial temperature of the iron bar:

Initial temperature of the iron bar = Final temperature - ΔT_iron

By following these steps, you should be able to find the initial temperature of the iron bar.