A 126.5 -g insulated aluminum cup at 18.00^∘ C is filled with 132.5 g of water at 46.25^∘ C . Af

A 126.5 -g insulated aluminum cup at 18.00^∘ C is filled...

Key Concepts

Conservation of Energy

The principle of conservation of energy states that energy in a closed system is neither created nor destroyed. When two bodies at different temperatures come into contact, the energy lost by the hotter body is exactly equal to the energy gained by the cooler body, allowing one to calculate the final equilibrium temperature by balancing the energy transfer.

Specific Heat Capacity

Specific heat capacity is a property of a substance that indicates the amount of heat required to change the temperature of a unit mass of the substance by one degree. It is an essential factor in heat transfer problems because it determines how much energy a substance can store or release during a temperature change, influencing the calculation of temperature changes and energy exchanges.

Thermal Equilibrium

Thermal equilibrium refers to the state reached by objects in thermal contact where they adopt the same temperature, resulting in no net exchange of heat. In problems like this, the final equilibrium temperature is determined by setting the net heat transfer between the substances to zero, meaning that the heat lost by one equals the heat gained by the other.

Entropy and Entropy Change

Entropy is a measure of the disorder or randomness in a system, and the change in entropy quantifies the dispersal of energy during a thermal process. In thermodynamic processes, especially involving heat transfer in isolated systems, the total change in entropy is calculated by integrating the heat transfer over temperature (using dS = dQ/T) for each component. This concept is crucial for understanding the second law of thermodynamics and the irreversible nature of real processes.

Transcript

00:01 Here we want to find the final temperature of the system as well as the total change in entropy of the system.

00:05 So we can say that the mass of the water times the specific heat of the water, times the initial temperature of the water minus the final temperature of the system, would be equal to the mass of the aluminum times the specific heat of the aluminum, times the final temperature of the system minus the initial temperature of the aluminum.

00:26 This is because essentially the heat lost by the water would be equal to the heat gained by the aluminum.

00:34 And so we can solve for the final temperature.

00:37 The final temperature would, of course, would rather, through algebraic manipulation, would be equal to the mass of the aluminum times the specific heat of the aluminum, times the initial temperature of the aluminum, plus the mass of the water, times the specific heat of water, times the initial temperature of the water, all divided by the mass of the aluminum, times the specific heat of the aluminum, plus the mass of the water, times the specific heat of the water.

01:06 And at this point, we can solve, so the final temperature would be equal to 0 .1265 kilograms times 900 joules per kilogram per degree celsius, times the initial temperature of the aluminum, 18 degrees celsius, plus mass of the water.

01:28 0 .1325 kilograms multiplied by 4 ,186 joules per kilogram per degree celsius, and then multiplied by the initial temperature of the water, 46 .25 degrees celsius.

01:49 And this will all be divided by, again, 0 .1265 times 900 plus 0 .1325 times 4 ,186.

02:05 We find that the final temperature is going to be equal to 41 .44 degrees celsius.

02:12 So this would be our answer for part a.

02:16 For part b, however, we need to find the total change in entropy...

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