Calculate the increase in entropy of the Universe when you add 20.0 g of 5.00^∘ C cream to 200 g

step 1 Define T1 temperature of temperature cream, that is 5 degrees Celsius, 278 Kelvin. Now, T2 tempe

Calculate the increase in entropy of the Universe when you...

Calculate the increase in entropy of the Universe when you add $20.0 \mathrm{g}$ of $5.00^{\circ} \mathrm{C}$ cream to $200 \mathrm{g}$ of $60.0^{\circ} \mathrm{C}$ coffee. Assume that the specific heats of cream and coffee are both $4.20 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$

Key Concepts

Thermal Equilibrium

Thermal equilibrium refers to the state in which two or more substances in thermal contact reach the same temperature, resulting in no net exchange of heat energy. The process of mixing the coffee and cream ultimately leads them to an equilibrium state, and calculating this final temperature is essential for determining the corresponding changes in entropy.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. This concept is crucial in calculating the energy exchanged during the temperature change of both the coffee and the cream, and thus in determining their respective contributions to the total entropy change.

Entropy

Entropy is a thermodynamic property that quantifies the degree of disorder or randomness in a system. In the context of this problem, the change in entropy when two substances at different temperatures interact is calculated by integrating the heat exchanged over temperature, reflecting how energy dispersion increases the disorder of the universe.

Second Law of Thermodynamics

The second law of thermodynamics states that for any spontaneous process, the total entropy of the universe increases. In this scenario, the mixing of hot coffee with cold cream is an irreversible process that results in an increase in the total entropy, demonstrating the natural tendency towards equilibrium and disorder.

Calorimetry

Calorimetry is the study and measurement of heat transfer during physical and chemical processes. It is used here to determine the final equilibrium temperature after mixing the cream and coffee by applying the conservation of energy principle, equating the heat lost by the hot substance to the heat gained by the cooler one.

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