I need to solve latent heat. It gives me the number of ice cubes and the mass in grams (7550 grams). It wants to know how many calories would burn turning the ice into body temperature water (if body temp is 37 degrees celsius.) It gives Lm of H2O=1,44 kcal.mol and cwater=1.0 cal/g*degrees celsius. I can't figure out how to set up this problem.
q = (mass ice x heat fusion) + [mass ice x specific heat H2O x Tfinal-Tinitial)]
heat fusion is 80 cal/g
So is the first part of the equation because it is in ice form and the second part because it is the change of temperature after it becomes water? And thank you for the answer.
One more question please. Do I need to convert to joules or can it be kept in cal/g? Thanks in advance
To solve this problem, we need to understand the concept of latent heat and apply the specific heat formula. Here's how you can approach it:
1. Start by calculating the amount of heat required to raise the temperature of the ice from its initial temperature to 0 degrees Celsius. As the ice is initially below its melting point, we need to consider the heat required to raise its temperature to 0 degrees Celsius before it starts melting.
- The specific heat capacity of ice (cice) is 1.0 cal/g*°C.
- The initial temperature of the ice is below its melting point (0°C), so let's assume it to be -10°C.
- The mass of the ice cubes given is 7550 grams.
- The formula to calculate the amount of heat required is Q = mcΔT (Q: heat energy, m: mass, c: specific heat capacity, ΔT: change in temperature).
Using the above information, calculate the heat required to raise the temperature of the ice to 0°C.
2. The next step is to calculate the amount of heat required to melt the ice cubes. Here, we need to use the concept of latent heat.
- The latent heat of fusion for water (Lm) is 1.44 kcal/mol.
- The number of moles of ice can be calculated using the molar mass of water (18.015 g/mol) and the given mass of ice cubes (7550 grams).
- The formula to calculate the amount of heat required is Q = nLm (Q: heat energy, n: number of moles, Lm: latent heat of fusion).
Calculate the heat required to melt the ice cubes.
3. Finally, calculate the amount of heat required to raise the temperature of the melted ice from 0°C to body temperature (37°C).
- The specific heat capacity of water (cwater) is 1.0 cal/g*°C.
- The formula to calculate the amount of heat required is Q = mcΔT (Q: heat energy, m: mass, c: specific heat capacity, ΔT: change in temperature).
Calculate the heat required to raise the temperature of the melted ice from 0°C to 37°C.
4. Add up the heat required in steps 1, 2, and 3 to get the total heat energy required to turn the ice into body temperature water.
Total heat energy = heat required in step 1 + heat required in step 2 + heat required in step 3.
Calculate this total heat energy to find out how many calories would burn turning the ice into body temperature water.