Which state in each of the following pairs has the higher entropy per mole of substance? (d) Water vapor at 150 °C and 1 atm or water vapor at 100 °C and 2 atm

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Entropy is a measure of the disorder or randomness in a system. In general, the higher the temperature and the lower the pressure, the higher the entropy.

Consider the effect of temperature: Higher temperature increases the kinetic energy of molecules, leading to greater disorder. Therefore, water vapor at 150 °C will have higher entropy than at 100 °C.

Consider the effect of pressure: Lower pressure allows molecules to spread out more, increasing disorder. Therefore, water vapor at 1 atm will have higher entropy than at 2 atm.

Compare the two conditions: Water vapor at 150 °C and 1 atm has both higher temperature and lower pressure compared to water vapor at 100 °C and 2 atm.

Conclude that water vapor at 150 °C and 1 atm has higher entropy per mole than water vapor at 100 °C and 2 atm.

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Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. Higher entropy indicates greater disorder and more available microstates, which is often associated with gases compared to liquids or solids.

Effect of Temperature on Entropy

Temperature significantly influences entropy; as temperature increases, the kinetic energy of particles also increases, leading to greater molecular motion and disorder. Therefore, at higher temperatures, substances generally exhibit higher entropy due to the increased number of accessible energy states for the molecules.

Effect of Pressure on Entropy

Pressure affects the entropy of gases, as increasing pressure typically reduces the volume available to gas molecules, thereby limiting their freedom of movement and reducing disorder. However, at constant temperature, a gas at lower pressure can have higher entropy than at higher pressure, especially if the temperature is also considered.