Latent Heat Problem? Not sure how to solve

[PBryan833]

Homework Statement

A window of a car is found to be covered with 0.8cm of ice. If the area of the window is 1 m2, and the ice is at -12 degrees Celsius, what is the minimum heat required to melt all the ice? Take the density of ice to be 900 kg/m3, the specific heat capacity of ice to be 0.5 cal/g*K, and the latent heat of fusion to be 80 cal/g. Answer in kcal.[/B]

Homework Equations

deltaQ=mcdeltaT
Latent Heat= deltaQ= Lm[/B]

The Attempt at a Solution

So first off, I am confused in terms of finding out the mass to use. I wasnt sure if it is .512 g by multiplying .8x.8.x8 for cm3, or if you are supposed to make 0.8cm into meters then get the volume of that and multiply it by 900kg/m3 and then make kg into grams. If it is the second method, then the mass would be .46 grams?

So then what i tried doing is add Q1 and Q2 to each other. Q1 for me was (0.512)(.5 cal/g K)(12) and then Q2 i have as (80 cal/g)(.512) Then i added these together to get 44.032 calories which would be 0.044032 kcal. This answer does not seem right however and I feel like it is too low. What am I doing wrong? Thank You So much

 

[NTW]

First of all, please correctly compute the volume of the ice in cm³. I remind you that you have a surface of 1 m² with a thickness of 0,8 cm. Once you have the volume, convert it to mass in grams by multiplying it by the density of the ice.

And once you have correctly calculated the mass, you can proceed with the heat that must be supplied...

 

[Chestermiller]

So first off, I am confused in terms of finding out the mass to use. I wasnt sure if it is .512 g by multiplying .8x.8.x8 for cm3, or if you are supposed to make 0.8cm into meters then get the volume of that and multiply it by 900kg/m3 and then make kg into grams. If it is the second method, then the mass would be .46 grams?

Method 2 is the correct approach, but your answer is wrong. Please show us your work.

So then what i tried doing is add Q1 and Q2 to each other. Q1 for me was (0.512)(.5 cal/g K)(12) and then Q2 i have as (80 cal/g)(.512) Then i added these together to get 44.032 calories which would be 0.044032 kcal. This answer does not seem right however and I feel like it is too low. What am I doing wrong? Thank You So much

Your approach here is correct, but, because your estimate of the mass is say low, so is this answer.

Chet

 

[PBryan833]

thank you both for the help!

 

[HalfLostAndSearching]

As a scientist, it is important to carefully consider all of the information provided in the problem and use appropriate equations to find a solution. In this case, the first step would be to convert the ice thickness from 0.8cm to meters, which would be 0.008m. Then, using the area of the window (1m2) and the ice thickness, we can calculate the volume of ice as 0.008m3. Multiplying this by the density of ice (900 kg/m3) gives us a mass of 7.2 kg.

Next, we can use the equation Q=mcΔT to find the heat required to raise the temperature of the ice from -12°C to 0°C. This would be (7.2 kg)(0.5 cal/g K)(12 K) = 43.2 cal = 0.0432 kcal.

Finally, we need to consider the heat required to melt the ice, which is given by Q=mL, where L is the latent heat of fusion (80 cal/g). So, the total heat required to melt all the ice would be (7.2 kg)(80 cal/g) = 576 cal = 0.576 kcal.

Adding these two values together, we get a total heat of 0.6192 kcal required to melt all the ice on the window. It is important to pay attention to units and make sure they all match up in the final answer.

In summary, to solve this latent heat problem, we first converted all units to the appropriate form, calculated the heat required to raise the temperature of the ice, and then added that to the heat required to melt the ice. I hope this explanation helps you better understand how to approach and solve similar problems in the future.