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The Ideal Gas

# The Ideal Gas - isothermal expansion The work done by the...

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The Ideal Gas Avogadro made the suggestion that all gases - under the same conditions of temperature and pressure - contain the same number of molecules. Reversely, if we take 1 mole samples of various gases, confine them in boxes of identical volume and hold them at the same temperature, we find that their measured pressures are nearly identical. Experiments showed that the gases obey the following relation (the ideal gas law ): where n is the number of moles of gas, and R is the gas constant . R has the same value for all gases: The temperature of the gas must always be expressed in absolute units (Kelvin). Using the ideal gas law we can calculate the work done by an ideal gas. Suppose a sample of n moles of an ideal gas is confined in an initial volume V i . The gas expands by moving a piston. Its final volume is V f . During the expansion the temperature T of the gas is kept constant (this process is called

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Unformatted text preview: isothermal expansion ). The work done by the expanding gas is given by The ideal gas law provides us with a relation between the pressure and the volume Since T is kept constant, the work done can be calculated easily Note: Sample Problem 18-1 A cylinder contains oxygen at 20 ° C and a pressure of 15 atm. at a volume of 12 l. The temperature is raised to 35 ° C , and the volume is reduced to 8.5 l. What is the final pressure of the gas ? The ideal gas law tells us that The initial state of the gas is specified by V i , p i and T i ; the final state of the gas is specified by V f , p f and T f . We conclude that Thus The temperature T in this formula must be expressed in Kelvin: T i = 293 K T f = 308 K The units for the volume and pressure can be left in l and atm. since only their ratio enter the equation. We conclude that p f = 22 atm....
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The Ideal Gas - isothermal expansion The work done by the...

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