Thermodynamics Equations Thermodynamics Equations Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. T hermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics. One of the fundamental thermodynamic equations is the description of thermodynamic work in analogy to mechanical work, or weight lifted through an elevation against gravity, as defined in 1824 by French physicist Sadi Carnot. Carnot used the phrase motive power for work. In the footnotes to his famous On the Motive Power of Fire, he states: “We use here the expression motive power to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.� With the inclusion of a unit of time in Carnot's definition, one arrives at the modern definition for power:
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A thermodynamic system is in equilibrium when it is no longer changing in time. This may happen in a very short time, or it may happen with glacial slowness. A thermodynamic system may be composed of many subsystems which may or may not be "insulated" from each other with respect to the various extensive quantities. If we have a thermodynamic system in equilibrium in which we relax some of its constraints, it will move to a new equilibrium state. The thermodynamic parameters may now be thought of as variables and the state may be thought of as a particular point in a space of thermodynamic parameters. The change in the state of the system can be seen as a path in this state space. This change is called a thermodynamic process. Thermodynamic equations are now used to express the relationships between the state parameters at these different equilibrium state. Thermodynamics Examples The evaporation of sweat from your body is an example of thermal equilibrium in action. Solution A :System :- The sweat Surroundings :- Your body + the rest of the universe q > 0 so, Heat flows into the system (sweat) from you in order to raise the kinetic energy of the sweat molecules enough to allow them to go from the liquid phase to the gas phase. Solution B System :- You Surroundings :- The sweat + the rest of the universe
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Q < 0 :- Heat flows out of the system (you) into the sweat. Since heat leaves your body this cools you down. This is the reason for our sweating. Example of thermal equilibrium :- Let us consider two beakers full of water. Then for one beaker, the temperature of water is above the normal room temperature, and for the other beaker it is below the normal room temperature. They are left on the table for sometime such that they both are not in contact with each other. If we check the beakers after some time, equilibrium for both the beakers is reached. As observed both the beakers of water are at the same temperature. The two beakers actually come in thermal equilibrium with the surroundings. Hence they are in thermal equilibrium with each other also and they are at the same temperature. Practice Problems Question 1: Suppose a man standing on top of a tower, 200m tall. He is holding a small, heavy ball that weighs 5kg. What would be the velocity of the ball be when it hits the ground assuming it was dropped on the ground with zero initial velocity? What would be the velocity of the ball be when it hits the ground assuming it was dropped on the ground with 20m/s? Question 2: Water is flowing at the rate of 2 litres per minute from a tap and a geyser is heating it such that the temperature rises from 23 to 77 degree centigrade. If the geyser is supplied and aided with a burner than find the rate of combustion of the fuel given the heat of combustion is 2 Ă&#x2014; 100000 J/g. Question 3: Why does the air pressure of the tire rises during driving? Question 4: Why the coolant used in nuclear plants should have more specific heat?
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