An aluminum can, with negligible heat capacity, is filled with 450 g of water at 0^∘ C and then

step 1 the system. And we can say that the mass of the hot water times the specific heat of water times

An aluminum can, with negligible heat capacity, is filled...

An aluminum can, with negligible heat capacity, is filled with 450 $\mathrm{g}$ of water at $0^{\circ} \mathrm{C}$ and then is brought into thermal contact with a similar can filled with 450 $\mathrm{g}$ of water at $50^{\circ} \mathrm{C}$ . Find the change in entropy of the system if no heat is allowed to exchange with the surroundings. Use $\Delta S=\int d Q / T$ .

An aluminum can, with negligible heat capacity, is filled with 450 $\mathrm{g}$ of water at $0^{\circ} \mathrm{C}$ and then is brought into thermal contact with a similar can filled with 450 $\mathrm{g}$ of water at $50^{\circ} \mathrm{C}$ . Find the change in entropy of the system if no heat is allowed
to exchange with the surroundings. Use $\Delta S=\int d Q / T$ .

Key Concepts

Entropy

Entropy is a fundamental concept in thermodynamics that quantifies the degree of disorder or randomness in a system. It provides a measure of the energy dispersal within a system when energy is exchanged in the form of heat. In any process, changes in entropy help determine the direction and spontaneity of that process.

Thermal Equilibrium

Thermal equilibrium occurs when two or more systems or objects in thermal contact reach a common temperature and no net heat flow occurs between them. In the context of mixing fluids or objects at different temperatures in an isolated system, the final equilibrium temperature is reached when the energy lost by the warmer component equals the energy gained by the cooler one.

Conservation of Energy

The principle of conservation of energy states that within an isolated system, energy can neither be created nor destroyed, only transferred or transformed. When two bodies at different temperatures are brought into contact, the heat lost by the hotter body must be exactly equal to the heat gained by the colder body, leading to a predictable final temperature.

Entropy Change Calculation

Entropy change for a system undergoing a temperature change can be calculated using the integral form ?S = ?(dQ/T). When the heat capacity is constant, this relationship simplifies to ?S = mc ln(T_final/T_initial). This formula is essential for determining the entropy changes for individual parts of the system as they move towards equilibrium.

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