Kinetic Theory and Thermodynamics

Kinetic Model for Ideal Gas The gas consists of molecules of mass m in ceaseless random motion The size of the molecules is negligible, in the sense that their diameters are much smaller than the average distance traveled between collisions The molecules do not interact, except that they make perfect elastic collisions when they are in contact

Ideal Gas Law

Zeroth Law of Thermodynamics The "zeroth law" states that if two systems are at the same time in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

The First Law of Thermodynamics Internal energy is defined as the energy associated with the random, disordered motion of molecules.

Second Law of Thermodynamics

PV Diagrams For a cyclic heat engine process, the PV diagram will be closed loop. The area inside the loop is a representation of the amount of work done during a cycle. Work is done only when the volume of the gas changes.

Heat Engines The engine takes energy from a hot reservoir and uses part of it to do work, but is constrained by the second law of thermodynamics to exhaust part of the energy to a cold reservoir. In the case of the automobile engine, the hot reservoir is the burning fuel and the cold reservoir is the environment to which the combustion products are exhausted.

Carnot Cycle The most efficient heat engine cycle is the Carnot cycle, consisting of two isothermal processes and two adiabatic processes. The Carnot cycle can be thought of as the most efficient heat engine cycle allowed by physical laws. In order to approach the Carnot efficiency, the processes involved in the heat engine cycle must be reversible and involve no change in entropy.

Sample Multiple Choice Question An ideal monatomic gas is compressed while its temperature is held constant. What happens to the internal energy of the has during this process, and why? A) It decreases because the gas does work on its surroundings. B) It decreases because the molecules of an ideal gas collide, C) It does not change because the internal energy of an ideal gas depends only on its temperature. D) It increases because work is done on the gas. E) It increases because the molecules travel a shorter path between collisions.

Correct Answer

(10 points) A cylinder with a movable frictionless piston contains an ideal gas that is initially in state 1 at 1 105 Pa, 373 K, and 0.25 m3. The gas is taken through a reversible thermodynamic cycle as shown in the PV diagram above. (a) Calculate the temperature of the gas when it is in the following states. i. State 2 ii. State 3 (b) Calculate the net work done on the gas during the cycle. (c) Was heat added to or removed from the gas during the cycle? ____ Added ____ Removed

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