Find the mass of iron heated to 85 degrees celcius that was added to 54.0 grams of water. The temperature of the water changed from 20 degrees celcius to 60 degrees celcius. The specific heat of the iron is 0.045 J/g degrees celcius
Note the correct spelling of celsius.
heat lost by Fe + heat gained by water = 0
[mass Fe x specific heat Fe x (Tfinal-Tintial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for the only unknown.
To find the mass of the iron, we can use the equation:
q = m * c * ΔT
where:
q = heat transferred (in Joules)
m = mass (in grams)
c = specific heat capacity (in J/g °C)
ΔT = change in temperature (in °C)
First, let's calculate the heat transferred to the water using the equation above.
q_water = m_water * c_water * ΔT_water
The mass of the water (m_water) is given as 54.0 grams.
The specific heat capacity of water (c_water) is approximately 4.184 J/g °C.
The change in temperature of the water (ΔT_water) is: 60 °C - 20 °C = 40 °C.
Plugging the values into the equation, we have:
q_water = 54.0 g * 4.184 J/g °C * 40 °C
Now, let's calculate the heat transferred to the iron using the same equation.
q_iron = m_iron * c_iron * ΔT_iron
The specific heat capacity of iron (c_iron) is given as 0.045 J/g °C.
The change in temperature of the iron (ΔT_iron) is: 85 °C - 20 °C = 65 °C.
Plugging the values into the equation, we have:
q_iron = m_iron * 0.045 J/g °C * 65 °C
Next, realize that the heat transferred from the iron to the water is equal to the heat transferred from the water to the iron:
q_water = q_iron
Therefore:
54.0 g * 4.184 J/g °C * 40 °C = m_iron * 0.045 J/g °C * 65 °C
Now, we can solve for the mass of the iron (m_iron):
m_iron = (54.0 g * 4.184 J/g °C * 40 °C) / (0.045 J/g °C * 65 °C)
Calculating the above expression:
m_iron ≈ 172.80 g
Therefore, the mass of the iron heated to 85 degrees Celsius is approximately 172.80 grams.
To find the mass of the iron, we need to use the formula for heat transfer:
q = m * c * ΔT
where:
q is the heat absorbed or released
m is the mass of the substance
c is the specific heat of the substance
ΔT is the change in temperature
First, let's calculate the heat absorbed by the water using the formula above:
q_water = m_water * c_water * ΔT_water
The specific heat capacity of water is approximately 4.18 J/g degrees Celsius. The change in temperature is:
ΔT_water = T_final_water - T_initial_water
= 60°C - 20°C
= 40°C
We can substitute these values into the equation to find the heat absorbed by the water:
q_water = m_water * c_water * ΔT_water
= 54.0 g * 4.18 J/g°C * 40°C
= 8923.2 J
Since the heat lost by the iron is equal to the heat gained by the water (assuming no heat is lost to the surroundings):
q_iron = -q_water = -8923.2 J
Now, let's find the mass of the iron using the equation for heat transfer:
q_iron = m_iron * c_iron * ΔT_iron
We know the specific heat capacity of iron is 0.045 J/g°C, and the change in temperature of the iron is:
ΔT_iron = T_final_iron - T_initial_iron
= 60°C - 85°C
= -25°C
Substituting these values into the equation, we get:
-8923.2 J = m_iron * 0.045 J/g°C * -25°C
Simplifying the equation further:
-8923.2 J = -1.125 * m_iron
Now, let's solve for m_iron:
m_iron = -8923.2 J / -1.125 g
= 7926.4 g
Therefore, the mass of the iron heated to 85 degrees Celsius that was added to 54.0 grams of water is 7926.4 grams.