two hundred fifty grams of iron is heated from 27 degree Celsius to 300 degree Celsius . how much ice can be melted and raised to a temperature of 27 degree Celsius by hot iron?
Figure the heat in the iron.
250*spchatFe*(300-27)
now the tricky part: the ice and water.
heat to melt ice+water
m*Lf + m*cwater*(27-0). This assumes the initial temperature of the ice was 0C.
set the two heats equal, and solve for mass ice/water m.
To calculate how much ice can be melted and then raised to a temperature of 27 degrees Celsius by the hot iron, we need some additional information.
First, we need to know the specific heat capacity of iron and ice. The specific heat capacity (C) is the amount of heat energy required to raise the temperature of a given substance by one degree Celsius per unit mass.
Next, we need to know the heat of fusion of ice, which is the amount of heat energy required to melt one gram of ice at 0 degrees Celsius without changing its temperature.
Once we have these values, we can use the following steps to calculate the amount of ice that can be melted and raised to 27 degrees Celsius:
1. Calculate the heat absorbed by the iron:
- Determine the change in temperature, ΔT, of the iron:
ΔT = Final temperature - Initial temperature
ΔT = 300°C - 27°C
- Calculate the heat absorbed by the iron, Q_iron:
Q_iron = C_iron * m_iron * ΔT
where C_iron is the specific heat capacity of iron and m_iron is the mass of iron.
2. Calculate the heat required to melt the ice:
- Calculate the heat required to melt one gram of ice, Q_fusion:
Q_fusion = heat of fusion of ice
- Calculate the mass of ice that can be melted, m_ice:
m_ice = Q_iron / Q_fusion
3. Calculate the heat required to raise the temperature of the melted ice to 27 degrees Celsius:
- Determine the change in temperature, ΔT_ice, of the ice:
ΔT_ice = 27°C - 0°C
- Calculate the heat required to raise the temperature of the ice, Q_ice:
Q_ice = C_ice * m_ice * ΔT_ice
where C_ice is the specific heat capacity of water (since the ice has now melted) and m_ice is the mass of melted ice.
4. Finally, calculate the total mass of ice that can be melted and raised to 27 degrees Celsius:
- Calculate the total mass of ice, m_total:
m_total = m_ice + m_ice
By following these steps and obtaining the specific heat capacities and heat of fusion values, you can find out how much ice can be melted and raised to 27 degrees Celsius by the hot iron.