a copper calorimeter of mass 150g was half filled with water of 300g and temperature 0c. 5g of ice at oc was added to the content, later some quantity of steel was passed into the mixture and temperature by 20c. calculate the quantities of steel added if the latent heat of vapourization of steel is 2.6*10^6jkg specific heat capacity of copper is 400jkgk1
You have some serious problems in this post. What's with the steel being added? Surely you mean steam. And when the "steel" was passed into the mixture and temperature (what); i.e., stayed the same, rose by 20 C, decreased by 20 C.
Is that heat capacity of steel or heat capacity of steam?
To calculate the quantity of steel added to the mixture, we can use the principle of conservation of energy and apply it to the change in heat. Here's how you can do it step by step:
1. Calculate the heat gained by the water to reach the final temperature:
- The specific heat capacity of water is 4200 J/kg°C.
- The mass of the water is 300 g.
- The initial temperature of the water is 0°C, and the final temperature is 20°C.
Q_water = m_water * c_water * ΔT_water
= 300 g * 4200 J/kg°C * (20°C - 0°C)
= 300 g * 4200 J/kg°C * 20°C
= 2,520,000 J
2. Calculate the heat gained by the copper calorimeter to reach the final temperature:
- The specific heat capacity of copper is 400 J/kg°C.
- The mass of the copper calorimeter is 150 g.
- The initial temperature of the copper calorimeter is 0°C, and the final temperature is 20°C.
Q_copper = m_copper * c_copper * ΔT_copper
= 150 g * 400 J/kg°C * (20°C - 0°C)
= 150 g * 400 J/kg°C * 20°C
= 1,200,000 J
3. Calculate the heat absorbed by the phase change of the ice:
- The latent heat of vaporization of steel is given as 2.6 * 10^6 J/kg.
- The mass of the ice that melts is 5 g.
Q_phase_change = m_ice * L
= 5 g * 2.6 * 10^6 J/kg
= 13,000,000 J
4. Calculate the total heat gained by the mixture:
Q_total = Q_water + Q_copper + Q_phase_change
= 2,520,000 J + 1,200,000 J + 13,000,000 J
= 16,720,000 J
5. Use the equation Q = mcΔT to find the quantity of steel added:
- Assume the specific heat capacity of steel (c_steel) as 450 J/kg°C.
- Let the mass of the steel added be "m_steel."
Q_steel = m_steel * c_steel * ΔT_steel
Rearranging the equation:
m_steel = Q_steel / (c_steel * ΔT_steel)
Since we don't have the values for Q_steel and ΔT_steel, we cannot calculate the exact quantity of steel added without additional information.