20. Heat and Temperature

Specific Heat & Temperature Changes

# Heating Cup of Water

Patrick Ford

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Everybody. So welcome back here. Let's take a look at this problem here. So we have a cup of water that we're gonna put on a hot plate, which is rated at 200 watts. Now, all of this energy from the hot plate is going into the water as heat energy. So let me just draw this real quick here. Imagine I have, you know, this is like my hot plate, it's like a little, you know, sort of like a stove or whatever, like a portable stove. And I've got this little cup of water that's here on the inside like this. So I've got my couple of water. And basically what happens is this hot plate is going to supply energy into this water as heat energy. So there's gonna be some cue that transfers in now. What we wanna do is take and we want to figure out how long it takes for the water to warm from 10 to 90°C here. So which variable is that we're actually looking for delta little T. That's time. Remember, don't confuse this with capital delta T. Because that's a change in temperature. So how do we figure out what this DELTA T. Is our Q equals M. Cat equation doesn't have time in it. But we're actually gonna use another equation that we saw earlier in physics because we have something here that's measured in units of power, which is wants. So remember that the power equation is just P equals W over delta T. That was the works supply over change in time. Now, remember work is also just energy. So another way to sort of say this is just the amount of energy that something requires or takes divided by the change in time. So this is really where my delta T. Comes from. So if I want to solve for this DELTA T. Here, all I'm gonna do is just trade places with the power of variable. So they're just gonna swap places and my delta T. Just becomes the energy divided by power. Right? So this is units of jewels and this is units of jewels per seconds. When you divide them, you're just gonna end up, you're gonna end up with seconds. Alright, so what's going on here then? What's the amount of energy that I need? Well again, if you think about this, the hotplate delivers all of this heat energy into the water and all of it goes into warming the water from 10 to 90 degrees Celsius. So really what happens is the E. In my power equation is actually just being transferred into the water as heat energy. It's just Q. So this E. Here just becomes Q. So my delta T. Equation just becomes Q. Overpay. Now, what happens is my delta T. I have an equation for Q. Remember the specific heat equation is just M. C. Times delta T divided by the power. So that's just what that becomes. And so now I can start head go ahead and plug everything in. So I've got the mass of the water, that's 0.3 kg, that's 0.3 then I need the specific heat of water which is 86. That's just here in this table right here. So I've got 41 86. Now, it's the change in the temperature. Remember that change in the temperature could be either in Celsius or kelvin, it doesn't matter which one you use, If I'm going from 10 to 90, that means that the change in temperature, that's big. T is equal to 80. Alright, so this is just gonna be 80 over here. And then finally, just divide by the power, I'm told that the electric hot plate here is rated for 200 watts. So this hot plate here is just p equals 200. So this is just gonna come 200 over here. And then what you end up with is you end up with one times 10 to the fifth when you work out the numerator divided by 200 you'll end up with delta T. Is equal to 500 seconds and that's just about eight and 8.3 repeating minutes. Alright, so we'll take about eight and roughly 8.5 minutes in order to warm this water from 10, which is like room temperature to about 90 which is almost boiling. Alright, so that's your final answer. Let me know if you guys have any questions for this

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