1.) 100 kJ of heat is added to 600g of zinc at 20 C and 75g of it melts. If the specific heat of zinc is 0.385 kJ/kg-C and it melts at 420 C. What is its heat of fusion?
2.) If all the heat lost by 1kg of water at 0 C when it turns into ice at 0 C could be burn into KE, What would be the speed of ice?
3.) A 1kg block of ice at 0 C falls into a lake water is also at 0 C, 0.010kg of ice melts. What was the minimum altitude from which the ice fall?
I'm confused with the formulas to use :( help please :)
Sure! I can help you understand the formulas to use for each of the questions. Let's break them down one by one:
1.) To find the heat of fusion, we need to know the amount of heat energy required to melt a certain mass of substance. The formula we can use is:
Heat of Fusion = (Heat Energy Input) / (Mass of Substance Melted)
In this case, the heat energy input is given as 100 kJ and the mass of the zinc melted is given as 75 g. However, we need to convert the mass to kilograms, so 75 g becomes 0.075 kg. Plugging these values into the formula, we get:
Heat of Fusion = 100 kJ / 0.075 kg = 1333.33 kJ/kg
Therefore, the heat of fusion of zinc is 1333.33 kJ/kg.
2.) To find the speed of ice when all the heat lost by 1 kg of water at 0 degrees Celsius is converted into kinetic energy, we need to use the equation for kinetic energy:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
We know the mass of the water is 1 kg, and since it turns into ice, the mass of the ice would still be 1 kg. The initial temperature of the water is 0 degrees Celsius, so the final temperature of the ice would also be 0 degrees Celsius.
Since the heat lost by the water is converted into kinetic energy, we can equate the heat lost to the change in kinetic energy. The formula for heat lost is:
Heat Lost = Mass * Specific Heat * Change in Temperature
In this case, the specific heat of water is approximately 4.18 kJ/kg-C, and the change in temperature is 0 degrees Celsius (since the water and ice are at the same temperature). Therefore, we can write:
1 kg * 4.18 kJ/kg-C * 0 degrees Celsius = (1/2) * 1 kg * velocity^2
Simplifying the equation, we get:
0 = (1/2) * velocity^2
Since the velocity cannot be negative, the speed of the ice would be 0 m/s.
3.) To find the minimum altitude from which the ice falls, we need to consider the energy changes during the process.
The initial potential energy of the ice block is given by:
Initial Potential Energy = mass * g * initial height
The final potential energy is given by:
Final Potential Energy = mass * g * final height
Since the ice melts, we need to also consider the energy required for the phase change. The heat energy required to melt the ice is given by:
Heat Energy Required = mass * Heat of Fusion
In this case, the mass of the ice melted is given as 0.010 kg. The heat of fusion can be calculated using the specific heat of ice, which is approximately 333.5 kJ/kg.
Plugging in the values, we can equate the initial potential energy, final potential energy, and heat energy required:
mass * g * initial height = mass * g * final height + mass * Heat of Fusion
Since the mass cancels out from both sides of the equation, we can simplify further:
initial height = final height + Heat of Fusion
Therefore, the minimum altitude from which the ice falls can be calculated using the equation above.
I hope this helps clarify the formulas and methods to solve the given problems!
1.) Q=mC(T-t)+mLf
Lf=Q-mC(T-t)/m
Lf= 23,889.15cal-(600g)(0.092cal/gdegC)(420degC-20degC)/75g
Lf=24.122cal/g
Convert so you can cancel the unit :)