(II) A 2.8 -kg piece of aluminum at 43.0^∘ C is placed in 1.0 kg of water in a Styrofoam contain

step 1 the net entropy of the surroundings, or rather of the system. So we can say that the mass of the

(II) A 2.8 -kg piece of aluminum at 43.0^∘ C is placed in...

Key Concepts

Entropy

Entropy is a state function that quantifies the degree of disorder or randomness in a system. In thermodynamics, it is defined through the relation dS = dQ_rev/T for reversible processes. In problems involving heat transfer, calculating the change in entropy involves integrating the amount of heat added or removed over the temperature at which the transfer occurs.

Heat Transfer

Heat transfer refers to the process by which thermal energy is exchanged between systems or objects due to a temperature difference. This concept underlies the transfer of energy between substances of differing initial temperatures, and it is central to determining how much the temperature of each substance changes, which in turn affects their entropy.

Conservation of Energy

The conservation of energy principle states that the total energy in an isolated system remains constant, meaning the energy lost by one part of the system must be gained by another. This is used in calorimetry to equate the heat lost by a hotter object to the heat gained by a cooler one, enabling the calculation of the final equilibrium temperature and subsequent entropy changes.

Specific Heat Capacity

Specific heat capacity is a property of a material that describes the amount of heat required to change the temperature of a unit mass of the substance by one degree. In thermodynamic calculations, such as those involving calorimetry, it is used to relate the heat transferred to the resulting temperature change in each substance.

Thermodynamic Equilibrium

Thermodynamic equilibrium is the state in which a system's properties such as temperature, pressure, and volume remain constant over time because the system's internal processes have balanced out. For entropy calculations, reaching equilibrium provides the necessary final state information to assess the overall change in entropy of the system.

Transcript

00:01 The net entropy of the surroundings, or rather of the system.

00:04 So we can say that the mass of the aluminum times the specific heat of the aluminum times the temperature of the aluminum minus the temperature final would be equal to the mass of the water times the specific heat of the water times the temperature final minus the temperature initial of the water.

00:22 And so we can say that the temperature final of the system would be equal to the mass of the aluminum times a specific heat of the aluminum multiplied by the initial temperature of the aluminum plus the mass of the water times the specific heat of the water times the initial temperature of the water 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.

00:46 Now we can solve.

00:47 So the final temperature of the system would be 2 .8 kilograms times 900 joules per kilogram per degree celsius multiplied by 43 degrees celsius, multiplied by 1 .0 kilograms times 4 ,186 joules per kilogram per degree celsius, multiplied by 20 degrees celsius.

01:16 And this will all be divided by 2 .8 times 900 plus 1 .0 times 4 ,186.

01:28 And we find that the temperature final of the system is 28 .64 degrees celsius.

01:35 Now, to find the net entropy of the system, this would be equal to the change in entropy of the aluminum plus the change in entropy of the water.

01:44 We can say that this is going to be equal to the integral from the temperature of the initial temperature of the water, of the aluminum rather, to the final temperature of the system of the change and the heat transfer of the aluminum, divided by the temperature at which it occurs, plus the temperature of the water, times the temperature, the final temperature of the system, times the change in heat transfer of the water, divided by t, the temperature, and so we can solve.

02:13 Delta s will then be equal to the mass of the aluminum times the specific heat of the aluminum, times the integral from tal to t final, dt over t, this is going to be plus the mass of the water times the specific heat of the water, times the integral from the initial temperature of the water to the final temperature of the system, dt over t once again...

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