What change in entropy occurs when a 27.9 -g ice cube at -12^∘ C is transformed into steam at 11

step 1 In this problem we're going to talk about entropy. So let's say that we have a situation where w

What change in entropy occurs when a 27.9 -g ice cube at...

Key Concepts

Latent Heat

Latent heat is the amount of energy absorbed or released by a substance during a phase change at constant temperature. It is used in calculating the entropy change during phase transitions by using the formula ?S = Q/T, where Q is the latent heat and T is the temperature during the phase change.

Heat Transfer and Specific Heat Capacity

Heating or cooling a substance involves transferring energy to or from it, which changes the temperature according to the substance’s specific heat capacity. The entropy change during such temperature changes is calculated by integrating the reversible heat transfer (dQ) over the temperature (T), highlighting the contribution of temperature-dependent energy changes.

Entropy

Entropy is a thermodynamic state function that measures the disorder or randomness in a system. It quantifies the number of specific ways in which a system may be arranged, often interpreted as the unavailability of a system’s energy to do work. Changes in entropy are calculated by considering the heat exchanged at different temperatures during a process.

Phase Transitions

Phase transitions involve changes in the state of matter, such as melting (solid to liquid) and vaporization (liquid to gas), where energy is absorbed or released without a change in temperature. These processes require the addition or removal of latent heat, and the associated entropy change is determined by dividing the latent heat by the constant transition temperature.

Transcript

00:01 In this problem we're going to talk about entropy.

00:03 So let's say that we have a situation where we have an object and a certain amount of heat q is transferred to the object or from the object.

00:16 And the entropy s, the entropy difference s, associated with this process is equal to the integral from t0 to t0 is the initial temperature and t is the final one.

00:29 Of delta q, this is the increment of heat at each temperature t divided by t.

00:40 Also we're going to need to remember that the heat necessary to raise the temperature of an object is m, the math of the object, times the specific heat, times the change in temperature.

00:55 While the latent heat, q, necessary to change the face of matter of the object, is the mass times the latent heat constant l.

01:07 For ice, the specific heat is equal to 2 ,040 joules per kilogram degree celsius.

01:21 For liquid water, c is 1 ,184 joules per kilogram degree celsius, and for water vapor, c is 1 ,996 joules per kilogram degree celsius.

01:46 Also, the latent heat of fusion for the water.

01:52 Fusion is the change in state of matter from liquid to solid or the other way around actually from solid to liquid i'm sorry it's equal to 3 .34 times 10 to the 5 joules per kilogram while the latent heat of vaporization is equal to 2 .26 times 10 to the 6th joules per kilogram.

02:25 Okay.

02:29 So what we have to do in our problem is to consider ice, a mass of 27 .9 grams of ice that starts at a temperature t0 of minus 12 degrees celsius and finishes as vapor at a temperature of of 115 degrees celsius.

02:54 And i'm going to find what is the total change in entropy, s.

02:59 So i'm going to divide s into five parts.

03:04 The first part is the entropy necessary to raise the temperature from minus 12 to 0.

03:11 Then s2 is the entropy necessary to melt the i's.

03:17 Then as 3 is the heat, the entropy necessary to raise the temperature to 100 degrees.

03:25 As 4 is the heat necessary to convert the water, the liquid water to gas, and as 5 is the heat necessary to, i'm sorry, the entropy necessary to raise the temperature of the gas to 115 degrees celsius.

03:47 So let's start by s1.

03:51 Notice that this is delta q over t.

03:57 Now delta q is mc times dt, since we're talking about arrays in temperature.

04:07 So this is mc times the natural algorithm of t divided by t0.

04:14 T in this process, the final temperature, is 0 degrees celsius...

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