You have a 1.00-L sample of hot water (90.0^∘ C) sitting open in a 25.0^∘ C room. Eventually the

step 1 Okay, this looks like sort of a different problem. We're asked to calculate the entropy change f

You have a 1.00-L sample of hot water (90.0^∘ C) sitting...

You have a $1.00-\mathrm{L}$ sample of hot water $\left(90.0^{\circ} \mathrm{C}\right)$ sitting open in a $25.0^{\circ} \mathrm{C}$ room. Eventually the water cools to $25.0^{\circ} \mathrm{C}$ while the temperature of the room remains unchanged. Calculate $\Delta S_{\text {surn }}$ for this process. Assume the density of water is $1.00 \mathrm{~g} / \mathrm{cm}^{3}$ over this temperature range, and the heat capacity of water is constant over this temperature range and equal to $75.4 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}$.

Key Concepts

Entropy Change

Entropy change is a measure of the disorder or randomness in a system. In thermodynamics, for a process involving heat transfer, the change in entropy can be found by integrating the infinitesimal heat transfer divided by temperature. When considering the surroundings, if the temperature is constant, the change in entropy is simply the negative of the heat involved divided by the constant temperature.

Thermal Reservoir

A thermal reservoir is a large system that can absorb or provide finite amounts of heat without undergoing a significant change in temperature. In problems where the surroundings are assumed to remain at a constant temperature (such as a room maintained at a fixed temperature), the surroundings can be treated as a thermal reservoir. This assumption simplifies the calculation of the surroundings' entropy change because the temperature in the denominator of the integral is constant.

Heat Transfer with Constant Heat Capacity

The concept of constant heat capacity allows for the simplification of calculating the heat exchanged during a process. It means that the heat capacity remains unchanged over the range of temperatures involved, which in turn permits the direct use of the formula Q = nC?T (or its mass-based equivalent) to find the total heat transferred. This is particularly useful in calculating changes in entropy when the system’s temperature changes, as it ensures that the relationship between heat and temperature change is linear.

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