The temperature of n moles of an ideal gas changes from to in a quasi-static adiabatic transition. Show that the work done by the gas is given by. A dilute gas expands quasi-statically to three times its initial volume. Is the final gas pressure greater for an isothermal or an adiabatic expansion? Does your answer depend on whether the gas is monatomic, diatomic, or polyatomic? Isothermal has a greater final pressure and does not depend on the type of gas. If the initial pressure and temperature were and K, respectively, what are the final pressure and temperature of the gas?
Use for the gas. On an adiabatic process of an ideal gas pressure, volume and temperature change such that is constant with for monatomic gas such as helium and for diatomic gas such as hydrogen at room temperature. Use numerical values to plot two isotherms of 1 mol of helium gas using ideal gas law and two adiabatic processes mediating between them.
Use for your plot. Two moles of a monatomic ideal gas such as helium is compressed adiabatically and reversibly from a state 3 atm, 5 L to a state with pressure 4 atm. Consider the process shown below. Why or why not? No, because heat was added for both parts AD and DC.
There is not enough information to figure out how much is from each segment of the path. A car tire contains of air at a pressure of about 32 psi. How much more internal energy does this gas have than the same volume has at zero gauge pressure which is equivalent to normal atmospheric pressure? A helium-filled toy balloon has a gauge pressure of 0. How much greater is the internal energy of the helium in the balloon than it would be at zero gauge pressure?
Steam to drive an old-fashioned steam locomotive is supplied at a constant gauge pressure of about psi to a piston with a 0. Note that this is the net work output, since gauge pressure is used. Is the answer the same as in part a? A hand-driven tire pump has a piston with a 2. What is the net work output of a heat engine that follows path ABDA in the preceding problem with a straight line from B to D?
Five moles of a monatomic ideal gas in a cylinder at is expanded isothermally from a volume of 5 L to 10 L. Four moles of a monatomic ideal gas in a cylinder at is expanded at constant pressure equal to 1 atm until its volume doubles. Helium gas is cooled from to by expanding from 40 atm to 1 atm. If there is 1. In an adiabatic process, oxygen gas in a container is compressed along a path that can be described by the following pressure in atm as a function of volume V, with :.
The initial and final volumes during the process were 2 L and 1. Find the amount of work done on the gas. A cylinder containing three moles of a monatomic ideal gas is heated at a constant pressure of 2 atm.
The temperature of the gas changes from K to K as a result of the expansion. Find work done a on the gas; and b by the gas. A cylinder containing three moles of nitrogen gas is heated at a constant pressure of 2 atm. Find work done a on the gas, and b by the gas by using van der Waals equation of state instead of ideal gas law. Two moles of a monatomic ideal gas such as oxygen is compressed adiabatically and reversibly from a state 3 atm, 5 L to a state with a pressure of 4 atm.
Assume and for the diatomic ideal gas in the conditions given. An insulated vessel contains 1. The gas initially occupies a volume of 5 L. As a result of the adiabatic expansion the pressure of the gas is reduced to 1 atm. One mole of an ideal monatomic gas occupies a volume of at a pressure of a What is the temperature of the gas? One mole of an ideal gas is initially in a chamber of volume and at a temperature of. What is the heat transferred for this case?
The insulated cylinder shown below is closed at both ends and contains an insulating piston that is free to move on frictionless bearings. The piston divides the chamber into two compartments containing gases A and B. Originally, each compartment has a volume of and contains a monatomic ideal gas at a temperature of and a pressure of 1.
Use the fact that the compression of B is adiabatic to determine the final volume of both gases. In a diesel engine, the fuel is ignited without a spark plug. Instead, air in a cylinder is compressed adiabatically to a temperature above the ignition temperature of the fuel; at the point of maximum compression, the fuel is injected into the cylinder. Suppose that air at is taken into the cylinder at a volume and then compressed adiabatically and quasi-statically to a temperature of and a volume If what is the ratio Note: In an operating diesel engine, the compression is not quasi-static.
Skip to content The First Law of Thermodynamics. Learning Objectives By the end of this section, you will be able to: Define adiabatic expansion of an ideal gas Demonstrate the qualitative difference between adiabatic and isothermal expansions. The gas in the left chamber expands freely into the right chamber when the membrane is punctured. When sand is removed from the piston one grain at a time, the gas expands adiabatically and quasi-statically in the insulated vessel.
Quasi-static adiabatic and isothermal expansions of an ideal gas. Solution For an adiabatic compression we have. Summary A quasi-static adiabatic expansion of an ideal gas produces a steeper pV curve than that of the corresponding isotherm. A realistic expansion can be adiabatic but rarely quasi-static. Key Equations Equation of state for a closed system Net work for a finite change in volume Internal energy of a system average total energy Internal energy of a monatomic ideal gas First law of thermodynamics Molar heat capacity at constant pressure Ratio of molar heat capacities Condition for an ideal gas in a quasi-static adiabatic process.
Conceptual Questions Is it possible for to be smaller than unity? No, it is always greater than 1. Problems A monatomic ideal gas undergoes a quasi-static adiabatic expansion in which its volume is doubled.
Additional Problems Consider the process shown below. Challenge Problems One mole of an ideal monatomic gas occupies a volume of at a pressure of a What is the temperature of the gas? Previous: Heat Capacities of an Ideal Gas. Therefore, when an ideal gas expands freely, its temperature does not change; this is also called a Joule expansion. The gas is made to expand quasi-statically by removing one grain of sand at a time from the top of the piston.
We are then left with. This equation is the condition that must be obeyed by an ideal gas in a quasi-static adiabatic process. In doing this, we find that. The slope of the curve at any point is. The slope of this curve is useful when we consider the second law of thermodynamics in the next chapter. This slope is. Gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position.
Note that in the actual operation of an automobile engine, the compression is not quasi-static, although we are making that assumption here. The negative sign on the work done indicates that the piston does work on the gas-air mixture.
0コメント