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IDEAL GAS BEHAVIOR THERMODYNAMICS OF GASES Objective: To understand how the Ideal Gas Law and the laws of thermodynamics are used together to fully understand the behavior of gases. Goals: 1. 2. Students will know the 1st law of thermodynamics Students will be able to use the Ideal Gas Law and the 1st law of thermodynamics to make basic calculations about gases under varying conditions. represents an overall kinetic energy of the gas and is recognized as wind. If the gas is enclosed in a cylinder there is no wind but merely randomized molecular motion. Thus all molecular motion is internal energy. Assuming that a gas stays in the gaseous state without phase change, the amount of energy required to cause a temperature change is given by: Q = MCT (eq. 1) Where: Vocabulary: Adiabatic, Isobaric, Isothermal, Isometric, Internal Energy Q = Energy (joules) M = Mass (kg) CP = Specific heat (CP, Cv) T = Temperature (Absolute) This is the change in internal energy. Temperature and Internal Energy: The internal energy of a gas varies directly with the temperature of the gas. At absolute zero (0 K), all molecular motion stops so that there is no energy within the gas at this point. As the randomized speed of the molecule increases so does the internal kinetic energy of the gas molecules. This increase in randomized kinetic energy is noted as an increased temperature Note: If molecular motion within a gas sample is not randomized (in all directions) and is instead all in a common direction, it does not represent internal energy and it does not affect the temperature. Instead, this Note: Within the natural range of temperatures, the specific heat of atmospheric air is approximately 1.007 kJ/kg K. This means that it takes 1.007 kJ of energy to raise 1 kg of air by 1 degree K. Activity: Students build Excel spreadsheet calculator to determine the heat difference between different temperatures with variables for mass and specific heat. 1ST Law of Thermodynamics The first law of thermodynamics states that energy is neither created or destroyed. The sum of all energies entering a system and all energies leaving a system represents a change in the total energy of a system. Activity: Students develop an Excel model to analyze change of internal energy for a system and the resulting temperature change. In physics we generally group energy into two forms: Heat and Work In this equation, heat is defined as the total of all energy entering or exiting the system by any means except by direct compression or expansion of the gas. Isobaric Work on a Gas: As we discussed earlier, work refers to energy specifically associated with expanding or compressing a gas. Consider a piston assembly as shown below. Work is defined as the energy added to or removed from a gas by either compressing or expanding the gas (i.e. a piston assembly) since this is the manner in which machines typically extract useful work from a gas. Force = F With this understanding, we can write the First Law of Thermodynamics as: U = Q + W Distance = D (eq. 2) Where: U = Internal Energy Q = Energy added or removed from a system by any means except for ‘work’. W = Work done by changing volume (compressing or expanding a cylinder). Questions: -What is the change in internal energy of a gas if 2,000 joules of work are done on the gas and 6,000 joules of work is allowed to exit the system by cooling? -The enclosed gas in the previous question is .02 kg of atmospheric air. If the gas starts at 308 K what is its final temperature? -How much heat is required to increase the temperature of 1.2 kg of air isometrically by 30 deg C? As a forec F pushes down on the piston through a distance D it compresses the gas. If the force is constant, then the work required to compress the gas is: W=FxD Which is the definition of work from classical mechanics. The Force required is equal to the pressure of the gas times the cross sectional area of the piston. Once again, if pressure remains constant, this becomes: W=PxAxD Note: A x D = change in volume, thus for an isobaric process: U = H + U or U = 0 + (-) W = PV (Eq 3) yielding: U < 0 For our system we use the convention that work done on the system (compression) has a positive value and work done by the system (expansion) has a negative value. Isothermal Work on a Gas: An isothermal system presents another unique situation. In this system the pressure is not constant but varies inversely with the volume. This lead to a work equation: W = Pavg V T I F F a r e Q u ic k T im ( Un c o m n e e d e d P dV e ™ a n d a p r e s s e d ) d e c o m p r e s s o r t o s e e t h is p ic t u r e . Summary: -The internal energy of a gas is directly related to the temperature of the gas. -The first law of thermodynamics: U = Q + W (Eq. 4) General Work on a Gas: All processes are not isobaric; in fact, this is an unusual system. The general solution equation is: W= Since, for an ideal gas, internal energy is directly proportional to temperature. Thus, this represents a decrease in temperature. (Eq. 5) This is a mathematical formula that is beyond the prerequisite knowledge for theis course so we will restrict our calculations to the two specific conditions covered here. Adiabatic Espansion: It is a fact that warm air rises yet, we also know that air gets colder at higher altitudes. The process by which air cools as it rises is called adiabatic expansion. As the air rises it does not lose heat (adiabatic) but it does expand due to the reduced pressure. Expanding air means that work is being taken out of the system. Based upon the 1st Law of Thermodynamics we see that, with H = 0 and W = negative, we have: -Gases are compressed throu a variety of processes. Specific processes of interest are: Adiabatic, Isobaric, Isothermal, Isometric -Adiabatic expansion causes air to cool as it rises and expands without losing heat. Homework: Students should develop a comprehensive Excel model to analyze the temperature and energy change of a gas for various heat and work conditions. Students may select their own variable parameters but are encouraged to include as much versatility as possible.