How much ice (in grams) would have to melt to lower the...

Key Concepts

Heat Transfer

Heat transfer is the process by which thermal energy is exchanged between substances or systems due to a temperature difference. It includes various mechanisms such as conduction, convection, and radiation, and is fundamental in analyzing how energy is distributed to cause temperature changes within and between materials.

Specific Heat Capacity

This is a property of a substance that indicates the amount of heat energy required to raise the temperature of a unit mass of the substance by one degree Celsius. It is key in determining how much energy is involved in changing the temperature of substances during heat exchange processes.

Latent Heat of Fusion

This is the amount of energy required to change a substance from the solid phase to the liquid phase at its melting point without changing its temperature. It plays a central role in problems involving phase changes, as it quantifies the energy absorbed or released during melting or freezing.

Energy Conservation

This principle states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the context of thermal processes, it means that the heat lost by one component of a system must be gained by another, making energy balance calculations essential in solving calorimetry problems.

Transcript

00:06 Okay, we're going to do problem 70 from chapter 11.

00:11 So that question is how much ice and grams would have to melt to lower the temperature of 352 milliliters of water from 25 degrees celsius to 5 degrees celsius.

00:23 Assume the density of water is 1 gram per millimeter.

00:27 So first of all, we don't know how much heat is going to be transferred.

00:33 So we have to find out the mass from the heat.

00:37 But for the heat first, we know that we have water, which i assume liquid water.

00:43 And its temperature we're assuming is dropping from 25 celsius to 5 degrees celsius, or that's a change of 20 kelvin.

00:52 Remember, kelvin and celsius units are the same.

00:56 They just have a different origin.

00:59 They're shifted relative to one another.

01:01 Kelvin starts at zero celsius starts at zero is in the freezing of ice, freezing of water.

01:09 Okay, so how much heat, that's going to be the amount of heat that we get from water, 35 ,000 milliliters of liquid water, dropping from 25 to 5 celsius.

01:23 Okay, so now that gives me a delta t of 25 minus 5 kelvin, which is equal to 20.

01:34 Kelvin that's the temperature change and 352 milliliters is actually 352 grams of water so we're going to use a mass of 352 grams it's a direct conversion just because we have water we're dealing with water so we've got 20 kelvin delta t we've got mass total mass water that we want change temperature for and now we need one more thing and the equation we want to use here for this is sure i move this down right so q was equal to mcs and use cs in your in your textbook times delta t and cs being the heat capacity in this case it's for liquid water so for c i'll just call it c here so we don't confuse anybody.

02:43 A lot of times i see written a c, but your text does this as well.

02:47 We'll see it's fine c.

02:49 Ok.

02:50 So for liquid water, we also have c is equal to, you can find this in chapter 11.

03:00 Just read through it.

03:02 So that is key capacity, which is actually pretty well -known number, 4 .184 joules per gram kelvin.

03:19 Okay, so now we have everything we need in this equation here.

03:22 So we're going to use that to get the amount of heat.

03:27 Okay, so the amount of heat is q equals the mass.

03:34 And normally this note that this m here, frequently that's the molar mass.

03:41 And that's what your textbook says, but we can also replace it with just a mass.

03:46 And that would still be still work out fine.

03:49 So the difference between m being a mass and m being a molar mass is that q will be units of energy per molar in the end rather than the absolute units of energy.

04:04 So the difference is if m is a mass and not a molar mass, you'll just get jewels.

04:10 If m is a molar mass and not a mass, you'll get jules per mole.

04:16 Okay? that said, we're going to calculate just the joules.

04:20 A total and absolute amount of energy total extensive quantity so in this case m is 352 get to the right color 352 grams times key capacity which is i got this right 4 .184 which is per gram, kelvin, and times the number we know, delta t, which is 20 kelvin...

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