A 50.0 -g ice cube at 0^∘ C is placed in 500 mL of water at 20^∘ C. Estimate the change in entr

A 50.0 -g ice cube at 0^∘ C is placed in 500 mL of water at...

Key Concepts

Thermodynamic Equilibrium

Thermodynamic equilibrium is a state where all parts of a system have the same temperature and no net flow of energy occurs. When substances at different temperatures or phases are combined, they eventually reach equilibrium, which is key to applying entropy calculations across the entire system. The final state, often used as a reference, allows for the correct evaluation of the total change in entropy for the system.

Energy Conservation

The principle of energy conservation, or the First Law of Thermodynamics, states that energy cannot be created or destroyed, only transformed from one form to another. In thermal processes, this concept is used to balance the heat lost by one part of the system with the heat gained by another. It is instrumental in determining the final equilibrium state of a system where different components, initially at different temperatures, exchange heat until a balance is reached.

Entropy

Entropy is a thermodynamic quantity that measures the degree of disorder or randomness in a system. It is fundamental to the Second Law of Thermodynamics and is calculated for processes by integrating the reversible transfer of heat over temperature, often expressed as ?S = ?(dQ/T). This concept is crucial for understanding how energy disperses during physical changes and chemical reactions, especially in systems undergoing phase changes or mixing at different temperatures.

Latent Heat of Fusion

The latent heat of fusion is the amount of energy required to change a substance from a solid phase to a liquid phase at its melting point without changing its temperature. It plays an essential role in processes involving melting or freezing, as energy added or removed from a system goes into changing the state rather than altering the temperature. In entropy calculations, this energy contributes to a change in the system's entropy during the phase transition.

Specific Heat Capacity

Specific heat capacity is the property of a material that quantifies the amount of heat required to raise the temperature of a unit mass of the substance by one degree Celsius (or one Kelvin). It is important in calculating the heat exchange when a substance undergoes a temperature change prior to a phase change, which in turn affects the entropy change of the system. It integrates with the concept of energy conservation during thermal exchanges in the system.

Transcript

00:01 Here we're going to quantify the entropy change in a chunk of ice that is dropped into slightly hotter water.

00:09 So the way entropy change is defined as a change is it is the amount of heat released or absorbed by a substance at a constant temperature.

00:27 So only changes can be quantified, not absolute entropy in this technique anyway.

00:38 So what's happening to the ice is it is absorbing heat in the amount of its mass times the latent heat of fusion of water into ice, ice into water.

00:54 And we can quantify that.

00:56 We know the mass is 0 .05 kilograms.

01:00 The latent heat of fusion of water is something very well known.

01:06 We can look it up, but it's a fairly large number here.

01:14 If we put all that together, we find out that the amount of heat absorbed is 1 .67 times 10 to the 4 joules.

01:29 Now, to use this equation, we have to have the temperature in kelvin.

01:38 So we'll go ahead and take our ice temperature, which is zero degrees centigrade, and of course we'll add 273 kelvin to that.

01:49 And so the entropy change of the ice is a positive change, which means the entropy of the ice increases, and that makes a lot of sense.

02:02 That there is more randomness once you break the crystalline bonds in the ice, those regularly ordered bonds.

02:20 And the unit is joules per kelvin.

02:24 That comes out to be about 61 .2 joules per kelvin.

02:31 Okay, now what about the water? well, here's the problem.

02:34 The water is the substance that is releasing the heat.

02:43 And it's changing its temperature as it releases that heat.

02:56 Okay, and the amount that it releases the heat is mc delta t.

03:04 So we do not have a constant temperature situation.

03:08 We do know that the entropy will decrease because delta s is negative.

03:15 But we have the situation as to what to use for the temperature.

03:21 And so we're going to assume that the entropy is changing in a linear fashion.

03:33 So we're going to kind of use the average.

03:37 And so we want to find out the average temperature between the beginning and the ending of the ice melting.

03:47 So we know that there's 1 .67 types 10 to the 4th jules that comes out of the water.

03:55 It has to do so for energy conservation.

03:59 But the temperature that we're going to use is the average between the initial and the final...

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