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Chapter 18: Problem 7

State the second law of thermodynamics in words and express it mathematically.

Short Answer

Expert verified
The second law of thermodynamics states the total entropy of an isolated system always increases over time. Mathematically, it can be expressed as \[\Delta S \geq \frac{Q}{T}\]

Step by step solution

01

Understanding the concept

The second law of thermodynamics largely deals with the concepts of energy and entropy. It states that in any closed system, the total entropy can never decrease over time. Entropy is often referred to as the state of disorder or chaos. It is a measure of randomness or disorder within a molecule or macroscopic system.
02

Defining the second law of thermodynamics in words

The second law of thermodynamics in words can be stated as: 'The total entropy of an isolated system can never decrease over time; it is constantly increasing because energy constantly flows from being concentrated, to becoming dispersed, spread out, wasted and useless. New energy cannot be created and high-grade energy is being destroyed.'
03

Express the second law of thermodynamics mathematically

Mathematically, this law can be expressed with the change in entropy \(\Delta S\) of a system is more than or equal to the heat exchanged by the system \(Q\) divided by the temperature of the system \(T\), which is \[\Delta S \geq \frac{Q}{T}\]

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Most popular questions from this chapter

The molar heat of vaporization of ethanol is \(39.3 \mathrm{~kJ} / \mathrm{mol}\) and the boiling point of ethanol is \(78.3^{\circ} \mathrm{C}\) Calculate \(\Delta S\) for the vaporization of \(0.50 \mathrm{~mol}\) ethanol.

Describe two ways that you could measure \(\Delta G^{\circ}\) of a reaction.

Find the temperatures at which reactions with the following \(\Delta H\) and \(\Delta S\) values would become spontaneous: (a) \(\Delta H=-126 \mathrm{~kJ} / \mathrm{mol}, \Delta S=84 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\) (b) \(\Delta H=-11.7 \mathrm{~kJ} / \mathrm{mol}, \Delta S=-105 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\).

Under what conditions does a substance have a standard entropy of zero? Can a substance ever have a negative standard entropy?

Ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) dissolves spontaneously and endothermically in water. What can you deduce about the sign of \(\Delta S\) for the solution process?
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