A 110-g insulated aluminum cup at 35^is filled with 150 g of water at 45^. After a few minutes,

step 1 Hello friends here it is given a insulated aluminum cup having the mass 110 gram that is 0 .11 k

A 110-g insulated aluminum cup at 35^is filled with 150 g of...

A 110-g insulated aluminum cup at 35$^\circ$C is filled with 150 g of water at 45$^\circ$C. After a few minutes, equilibrium is reached. ($a$) Determine the final temperature, and ($b$) estimate the
total change in entropy.

Key Concepts

Entropy Change

Entropy change is a measure of the disorder or randomness in a thermodynamic system and quantifies the energy dispersal that occurs during a process. In thermal processes, the change in entropy is calculated using the relation between heat transfer and temperature, often via the integral of ?Q/T, and helps determine the degree of irreversibility in the process.

Specific Heat Capacity

Specific heat capacity is a material property that indicates how much energy is required to raise the temperature of a unit mass of a substance by one degree. It plays a key role in calculating the amount of heat exchanged during temperature changes and is essential for setting up energy balances in mixing processes.

Thermal Equilibrium

Thermal equilibrium is the state reached when two or more objects at different temperatures, upon coming into thermal contact, exchange energy until they all attain a common temperature. This concept is fundamental in thermal physics as it governs the final state of systems where heat transfer occurs and no net energy transfer exists between the parts.

Conservation of Energy in Thermal Systems

The principle of energy conservation in thermal systems states that, in an isolated system, the total energy remains constant even as heat is exchanged between bodies. This principle is used to determine the final equilibrium temperature by ensuring that the heat lost by one part of the system is equal to the heat gained by another.

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