(a) How much heat transfer is necessary to raise the temperature of a 0.200 -kg piece of ice fro

(a) How much heat transfer is necessary to raise the...

Key Concepts

Heat Transfer Rate

The heat transfer rate is the amount of energy transferred per unit time, often measured in watts or kilojoules per second. It is important for determining the time necessary to achieve a certain energy transfer, particularly when the total energy needed for heating and phase transitions is known.

Temperature-Time Graph

This graph represents the change in temperature of a substance over time during a heating or cooling process. It typically shows linear segments corresponding to temperature changes at constant specific heat capacity and horizontal plateaus during phase transitions, where the temperature remains constant despite continued energy input.

Specific Heat Capacity

This concept describes the amount of heat required to raise the temperature of a unit mass of a substance by one degree in temperature. It is crucial when calculating the energy needed to change the temperature of a substance during a heating or cooling process without a phase change.

Latent Heat

Latent heat refers to the energy absorbed or released by a substance during a phase change, such as melting or vaporization, at a constant temperature and pressure. This concept is essential for calculating the total energy required when a substance undergoes phase transitions in addition to temperature changes.

Transcript

00:01 Now this question we are heating a ice, a piece of ice of mass 0 .2 kilograms from temperature of negative 20 degrees all the way to 130 degrees.

00:21 And we want to make eventually a graph of temperature versus time for this process.

00:29 Now we know that in between all of this there's a few different steps.

00:35 So from minus 20 degrees to 0, this is just when it's solid, when it's ice, the amount of energy that's gained is basically mc times the heat capacity of ice times delta t.

01:04 Then from zero degrees, there is a phase change, right, where it converts from ice to water.

01:15 And with that we will need the latent heat of fusion.

01:27 This latent heat of fusion of water.

01:34 It's about 3 .34 joules per gram.

01:50 What about 3 .34 kilojoules per kilogram? then we have also latent heat of vaporization.

02:03 Which is when it converts to steam this is 2 .23 times 10 power 6 juice per kilogram so at this first face change we're looking at m times the latent heat of fusion there's from here from 0 degrees to 100 degrees it's just gain mc but this heat capacity is the liquid water times delta t there 100 degrees there is a phase change of m times the later heat of vaporization then finally from 100 degrees to 130 it's just m times heat capacity of steam times delta t so we've broken down this into these five different steps we're gonna put that into our graph all right but first of all, we'll need to find what are these respective values.

03:27 So for the ice, portion, let me just label this as 1, 2, 3 ,45, right? so for the first one, the capacity of ice is 2 .90.

04:06 The change in temperature is 20 degrees.

04:23 So this is the total amount of energy.

04:27 We know that the rates of heat transfer, to the ice is 20 kilojoules, so 20 times 10 about 3 joules per second.

04:42 So we're using this, we can actually find what is the time taken, right? the time taken for this first step to complete will be taking 8360 divided by 20 times 10 times 3.

05:06 So about 0 .418 seconds.

05:26 Now for the second step, take the mass multiplied by the latency of fusion.

05:42 It's given as 334.

06:16 So this the amount of energy and once again we can find the time taken by just dividing by 20 ,000.

06:27 So this will take about 3 .34 seconds.

06:37 For the third part of this, we are looking at from 0 to 100 degrees in water.

06:57 So for water, the heat capacity is 4186, juice per kilogram per degree celsius.

07:04 Delta t is 100.

07:18 I can find a time taken.

07:22 It's about 4186, sorry, 4 .186 or 4 .19 seconds.

07:38 Then we have the conversion into steam, latent heat of vaporization.

07:50 The entire vaporization is given as 2 .23.

08:03 It's about 6.

08:19 So from here the time taken, that's divided this by 20 ,000, at about 22 .3 seconds.

08:49 And the last part would be the steam, increasing the temperature from 100 to 130 degrees.

09:09 So the heat capacity for steam 2 .0 .20.

09:18 And then the change in temperature will be 30 degrees, right? it's from 100 to 130...

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