BASIC OF THERMAL ENGINEERING

1. 1. Recall or state the first and second laws of thermodynamics. The first law is (change in internal energy) = (change in heat content) - (amount of work done by the system on its surroundings). Use the Greek letter delta (") to represent small changes, and write this more briefly as "U = "Q - P"V. The second law states in part that "S = "Q/T, where "Q is the increase in the system's heat content. If the system cools, then by convention "S is negative. T must here use an absolute temperature scale, meaning that its value at zero is where microscopic kinetic motion from heat stops.
2. 
   
   2. Rewrite "S = "Q/T so that you can introduce it into the first law. In other words, rewrite it as 
   Q= T"S.
3. 
   
   3. Introduce the result of Step 2 into the first law of thermodynamics. In other words, "U = "Q - P"V becomes "U = T"S - P"V. This is the fundamental thermodynamic relation.

TIPS

• The fundamental thermodynamic relation can also be derived from first principles. Specifically, the second law is not a fundamental definition of entropy. The definition of entropy in terms of the number of quantum states in a small range of internal energy is more fundamental. See Reif's "Fundamentals of Statistical and Thermal Dynamics" for a derivation.
• Note that the first law includes the relation P"V, not V"P. To understand this, recall the definition of work. Work requires a force to cause movement over a distance. For example, if you hold a weight in the air so that it doesn't move, you aren't doing work on it, though you grow increasingly tired from the effort. Likewise, V has to change for the system to actually do work on its surroundings.

Thermodynamic Effects of Water on Melting Ice

In addition to being one of the most abundant substances on Earth, water has interesting thermodynamic properties. For example, when it freezes, ice expands, taking up more space than the original volume of water did. Warm water melts ice much faster than warm air. Ice absorbs relatively large amounts of heat before it melts, making it handy for keeping things cold.

Heat Transfer

Heat moves 26 times faster to ice from water than from air of the same temperature. This happens because water is denser than air. Ice surrounded by water will melt faster than by air. Other factors that influence heat transfer include temperature and motion. Hot water will melt ice faster than warm water, and moving water melts it faster than still water.

Equilibrium

Water and ice can come to the same temperature, 32 F or 0 C. Scientists say an ice-water mixture at this temperature is at thermal equilibrium. In theory, if no heat enters or leaves the container, the same amounts of each water state can continue indefinitely. Small amounts of the water will freeze, and ice will melt, but the total amounts of each will not change. In reality, however, one state usually prevails, turning to either all water or ice.

Expansion

Water has the odd property of expanding when it freezes to ice. Most substances expand only when they become hotter, but water molecules line up and crystallize as they cool, taking up more room. If you have ice in a container of water, the total volume of the contents will decrease as the ice melts.

Phase Change

Melting ice undergoes a phase change from solid to liquid. Molecules in the ice must absorb enough energy to release themselves from the ice crystal and move freely as water. It takes .51 calories of energy to raise the temperature of one gram of ice 1 C. However, when it reaches the melting point, 0 C or 32 F, ice needs 80 calories per gram to turn into water. This means that water surrounding ice must deliver a great deal of heat energy in order to melt it.