The enthalpy of evaporation of water is 40.67 kJ/mol. Sunlight striking Earth's surface supplies 168 W per square meter (1 W = 1 watt = 1 J/s). (b) The specific heat capacity of liquid water is 4.184 J/g°C. If the initial surface temperature of a 1.00 square meter patch of ocean is 26 °C, what is its final temperature after being in sunlight for 12 h, assuming no phase changes and assuming that sunlight penetrates uniformly to depth of 10.0 cm?

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Welcome back everyone. We're told that the sun hits the earth providing 172 watts per square meter of energy. We have an area of 1.29 square meters for our solid sample with an initial temperature of negative 3.80 degrees Celsius and the sample is placed under the sun for 50 hours. We're told that the sun will uniformly penetrate the sample with a depth of 1.50 centimeters and it does not melt. And we need to calculate the final temperature of our sample. Were given the entropy of fusion of our liquid sample and the specific key capacity of our solid sample equal to this value here. So for our first part of our solution, we want to find energy and units of kilo jewels right now we know that our energy is equal to 172 watts per square meter from the sun according to the prompt. And so we want to go ahead and cancel our units of watts by recalling that it's equivalent to a dual per second. And so this will allow us to cancel out watts, leaving us with the final energy of 172 jewels per meter squared times seconds. And now because we need kilo jules, we're going to take our energy which we set is equal to jewels per meter squared times seconds. And we're going to multiply by the following conversion factor where we are given an area from the prompt of 1.29 square meters, which we will place over one, which will allow us to get rid of that square meter unit. Next we want to go ahead and focus on getting rid of that unit for time and according to the prompt, we have our sample left out in the sun for 15 hours. So we're going to get rid of hours before seconds and we should recall that for one hour. We have 60 minutes. This will allow us to cancel out ours and now we can get rid of minutes and seconds by recalling that in one minute. We have 60 seconds. And so now we can cancel out seconds as well as minutes. And we can get or focus on getting from jules, tequila jewels. So we should recall that our prefix kilo tells us we have 10 to the third power jewels for one kg jule. And now we can cancel out jules leaving us with kayla jewels as a unit of energy. And this will allow us to say that our energy is equal to a value in our calculators of 11,981 0.52 kg jewels. Now that we have our energy and kayla jewels, we want to move to step two of the solution which is finding the mass of our sample in its solid form. And so we would say that from the prompt we have an area of 1.29 square meters which is multiplied by its depth according to the prompt of 1.50 centimeters. And so we want to get rid of that square meter term. So we should recall that for one square meter. We have 100 squared centimeters squared. And so this allows us to cancel out square meters. And now we have centimeters and actually sorry about that. So we want square meters to be in the denominator to cancel it out. And so we would say that for one square meter in the denominator we have squared centimeters squared. And so now that we have squared meters in the denominator, we can cancel it out with square meters in the numerator. And now it's clear to see that we have centimeters being multiplied by squared centimeters, which actually gives us cubic centimeters. And so we can move into our next conversion factor to go from a cubic centimeter, which will allow us to go into grams for the mass of our sample. And we should recall that one cc is equal to 0.99987 g. So now we're able to cancel out cubic centimeters here with cubic centimeters in the denominator. And we're left with grams as our final unit. And this will give us a mass of 19, 0.4845 g of our sample. And now that we have the mass of our sample. We can move into Part three of our solution which is finding final temperature. And so we would take that mass. Or sorry. The energy above which is 11,981.52 kg jewels. And we want to go back into jewels for energy. So sorry about that. That is 0.52 kg jewels. So to go from kilo jewels, two jewels are prefix kilo tells us we have 10 to the third power jewels for one kg jule. Now we're able to cancel out kilo jules and we want to focus next on incorporating the specific heat capacity to cancel out jewels. And so from the prompt we're told that our specific heat capacity is 2. jewels. And then in our numerator we'll just write per one g times degrees Celsius. And so now we're able to cancel out jewels And now we want to be left with our temperature term in Celsius. So we need to get rid of grams. So we should go ahead and plug in our mass that we calculated above as a conversion factor. Where we determine that we have a mass of 19,347 10. g For our single sample here or for one mole of our sample. So we can now cancel out gramps and we're left with degrees Celsius as our final unit here. And so in our calculators. This will give us a value of temperature equal to 304.76°C. And this would be our final answer here as the final temperature of our solid sample after it's left in the sun for 15 hours. So I hope that everything I reviewed was clear. If you have any questions, leave them down below and I will see everyone in the next practice video.

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Key Concepts

Enthalpy of Evaporation

Specific Heat Capacity

Energy Transfer from Sunlight