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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

A carbon monoxide (CO) crystal is found to have entropy greater than zero at absolute zero of temperature. Give two possible explanations for this observation.

Which of the following are not state functions: \(S, H\) \(q, w, T ?\)

Consider the following reaction at \(25^{\circ} \mathrm{C}\) : $$ \mathrm{Fe}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{Fe}^{2+}(a q)+2 \mathrm{OH}^{-}(a q) $$ Calculate \(\Delta G^{\circ}\) for the reaction. \(K_{\mathrm{sp}}\) for \(\mathrm{Fe}(\mathrm{OH})_{2}\) is \(1.6 \times 10^{-14}\).

Use the following data to determine the normal boiling point, in kelvins, of mercury. What assumptions must you make in order to do the calculation? $$ \begin{aligned} \mathrm{Hg}(l): & \Delta H_{\mathrm{f}}^{\circ} &=0 \text { (by definition) } \\\ & S^{\circ} &=77.4 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol} \\ \mathrm{Hg}(g): & \Delta H_{\mathrm{f}}^{\circ} &=60.78 \mathrm{~kJ} / \mathrm{mol} \\ & S^{\circ} &=174.7 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol} \end{aligned} $$

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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