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Chapter 9: Problem 4

What thermodynamic condition must be met for a state of equilibrium to exist?

Short Answer

Expert verified
Answer: The main thermodynamic condition for a state of equilibrium is that the total change in its internal energy, 鈭哢, should be zero (鈭哢 = 0). When this condition is met, the system remains in a stable steady state with no net flow of energy or matter across its boundaries and exhibits constant macroscopic properties like temperature, pressure, and volume.

Step by step solution

01

Define Thermodynamic Equilibrium

In thermodynamics, a system is said to be in a state of equilibrium when it is at a stable steady state, with no net flow of energy or matter across its boundaries. At equilibrium, the macroscopic properties of the system, such as temperature, pressure, and volume, remain constant over time.
02

Identify the Conditions for Equilibrium

In order for a system to be in a state of thermodynamic equilibrium, the following conditions must be met: 1. Mechanical equilibrium: No unbalanced forces should exist within the system or across its boundaries. This results in the system having a constant pressure and volume. 2. Thermal equilibrium: No net flow of heat should occur within the system or between the system and its surroundings. This results in the system having a constant temperature. 3. Chemical equilibrium: There should be no net flow of matter within the system, and the composition of the system should remain constant. 4. Radiative equilibrium: The amount of incoming and outgoing radiation in the system should be equal. It is worth noting that all four of these conditions should be met simultaneously for a system to be in a complete state of thermodynamic equilibrium.
03

Main Thermodynamic Condition for Equilibrium

Among these conditions, the most important one to ensure a state of equilibrium is the balance of energy. In thermodynamics, this is expressed by the principle of minimum energy, stating that a system will attain equilibrium when its energy is minimized. The key thermodynamic condition for a system to reach equilibrium is that the total change in its internal energy, 鈭哢, should be zero. Mathematically, this condition can be written as: 鈭哢 = 0 When this condition is met, there will be no driving force for the system to undergo any spontaneous change, and it will remain in a stable state of equilibrium.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mechanical Equilibrium
Mechanical equilibrium plays a crucial role in establishing a state of overall equilibrium in a thermodynamic system. When a system is in mechanical equilibrium, there are no unbalanced forces acting upon it. This means that the pressure throughout the system is consistent and stable.
For instance, think of a balloon. When the balloon is neither expanding nor collapsing, it is in mechanical equilibrium. The pressure inside pulling outward is balanced by the pressure outside pushing inward.

Key points to remember about mechanical equilibrium:
  • No unbalanced forces within the system.
  • Constant pressure across the system.
  • Contributes to the overall stability of the system.
Mechanical equilibrium is foundational because it ensures that the physical structure of the system remains unaltered over time.
Thermal Equilibrium
Thermal equilibrium is that happy state where a system has achieved a uniform temperature throughout, meaning there's no net heat flow. This is essential for achieving true equilibrium because temperature variances can drive energy changes.
Imagine heating one part of a metal rod. Over time, heat will disperse along the rod until it's evenly distributed, resulting in thermal equilibrium.

Important aspects of thermal equilibrium include:
  • No net heat transfer within the system or with surroundings.
  • Uniform temperature across the system.
  • Ensures consistent energy distribution.
This concept is very significant as temperature differences usually lead to energy flow, disturbing equilibrium.
Chemical Equilibrium
Chemical equilibrium is achieved when a chemical reaction occurs and the concentration of reactants and products stabilizes over time. No net change in their amounts takes place after this point.
If you've mixed vinegar and baking soda, you've witnessed a reaction reaching chemical equilibrium once all observable changes cease.

Here are the vital points of chemical equilibrium:
  • Net reaction rates forward and backward are equal.
  • Concentration of all chemical species in the reaction is constant.
  • No further visible change in the system.
This balance means that the movement of matter within the system does not create any further net change, maintaining the system鈥檚 compositional stability.
Radiative Equilibrium
Radiative equilibrium is an interesting state where the energy radiated into a system is exactly balanced by the energy radiated out. This condition is especially relevant in atmospheric science and astrophysics.
Imagine Earth receiving sunlight. To maintain radiative equilibrium, Earth must radiate an equivalent amount of energy back into space.

Characteristics of radiative equilibrium include:
  • Energy received and emitted are equal.
  • Prevents energy buildup within the system.
  • Ensures a stable thermal environment.
Achieving radiative equilibrium is crucial for avoiding drastic temperature changes due to energy imbalance.

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Most popular questions from this chapter

Figure 9.36 is the tin-gold phase diagram, for which only single-phase regions are labeled. Specify temperature-composition points at which all eutectics, eutectoids, peritectics, and congruent phase transformations occur. Also, for each, write the reaction upon cooling.

For a lead-tin alloy of composition 80 wt\(\%\) \(\mathrm{Sn}-20 \mathrm{wt} \% \mathrm{Pb}\) and at \(180^{\circ} \mathrm{C}\left(355^{\circ} \mathrm{F}\right)\) do the following: (a) Determine the mass fractions of \(\alpha\) and \(\beta\) phases. (b) Determine the mass fractions of primary \(\beta\) and eutectic microconstituents. (c) Determine the mass fraction of eutectic \(\beta\)

Is it possible to have a magnesium-lead alloy in which the mass fractions of primary \(\alpha\) and total \(\alpha\) are 0.60 and \(0.85,\) respectively, at \(460^{\circ} \mathrm{C}\) \(\left(860^{\circ} \mathrm{F}\right) ?\) Why or why not?

Given here are the solidus and liquidus temperatures for the germanium-silicon system. Construct the phase diagram for this system and label each region. $$ \begin{array}{ccc} \hline \begin{array}{c} \text { Composition } \\ (\boldsymbol{w t} \% \text { Si) } \end{array} & \begin{array}{c} \text { Solidus } \\ \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) \end{array} & \begin{array}{c} \text { Liquidus } \\ \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) \end{array} \\ \hline 0 & 938 & 938 \\ 10 & 1005 & 1147 \\ 20 & 1065 & 1226 \\ 30 & 1123 & 1278 \\ 40 & 1178 & 1315 \\ 50 & 1232 & 1346 \\ 60 & 1282 & 1367 \\ 70 & 1326 & 1385 \\ 80 & 1359 & 1397 \\ 90 & 1390 & 1408 \\ 100 & 1414 & 1414 \\ \hline \end{array} $$

Briefly explain why, upon solidification, an alloy of eutectic composition forms a microstructure consisting of alternating layers of the two solid phases.
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