seventu grams of a piece of iron at 95 degree celsius is dropped into a copper calorimeter containing 150 grams of water at 20 degree celsius. the mass of copper calorimeter is 90 grams the final temperature of the mixture is 25 degree celsius. determine the specific heat of iron.

The sum of heats gained will be zero.

Heat gained is defined as mass*specheat*(tf-ti)

HeatgainedIron+HeatgainedCu+heatgainedwater=0

70*Ciron*(25-95)+150*Cwater*(25-20)+90*ccopper*(25-20)=0

solve for ciron.

To determine the specific heat of iron, we need to use the principle of conservation of energy. The heat lost by the iron will be equal to the heat gained by the water and the calorimeter.

We can use the formula:

Heat lost by the iron = Heat gained by the water + Heat gained by the calorimeter

Now let's break down the heat gained and lost using the formula:

1. Heat Lost by the iron:
The formula to calculate the heat lost is Q = mcΔT, where Q is the heat lost, m is the mass, c is the specific heat, and ΔT is the change in temperature.

So, the heat lost by the iron can be calculated as:
Q_lost = m_iron * c_iron * ΔT_iron

Given:
Mass of iron (m_iron) = 7 grams (convert 7 grams to kg)
ΔT_iron = final temperature - initial temperature = 25°C - 95°C = -70°C (remember to use Kelvin if calculating absolute temperatures)

2. Heat Gained by the water:
The formula to calculate the heat gained is Q = mcΔT, where Q is the heat gained, m is the mass, c is the specific heat, and ΔT is the change in temperature.

So, the heat gained by the water can be calculated as:
Q_water = m_water * c_water * ΔT_water

Given:
Mass of water (m_water) = 150 grams (convert 150 grams to kg)
ΔT_water = final temperature - initial temperature = 25°C - 20°C = 5°C (remember to use Kelvin if calculating absolute temperatures)

3. Heat Gained by the calorimeter:
The heat gained by the calorimeter can be calculated using the same formula as heat gained:

So, the heat gained by the calorimeter can be calculated as:
Q_calorimeter = m_calorimeter * c_calorimeter * ΔT_calorimeter

Given:
Mass of calorimeter (m_calorimeter) = 90 grams (convert 90 grams to kg)
ΔT_calorimeter = final temperature - initial temperature = 25°C - 20°C = 5°C (remember to use Kelvin if calculating absolute temperatures)

We know that the heat lost by the iron is equal to the sum of the heat gained by the water and the calorimeter:

Q_lost = Q_water + Q_calorimeter

Now we can substitute the values into the equation and solve for the specific heat of iron (c_iron):

m_iron * c_iron * ΔT_iron = m_water * c_water * ΔT_water + m_calorimeter * c_calorimeter * ΔT_calorimeter

Rearrange the equation to solve for c_iron:

c_iron = (m_water * c_water * ΔT_water + m_calorimeter * c_calorimeter * ΔT_calorimeter) / (m_iron * ΔT_iron)

Now plug in the values and calculate c_iron.