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phys124s11-hw10

# phys124s11-hw10 - HW 10 Solutions Introduction to the Ideal...

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1 HW 10 Solutions Introduction to the Ideal Gas Law a) A gas sample enclosed in a rigid metal container at room temperature (20 0 C) has an absolute pressure p 1 . The container is immersed in hot water until it warms to 40 0 C. What is the new absolute pressure p 2 ? 2 2 1 1 1 313 293 T PV nRT P P P T = = = . This modest temperature increase (in absolute terms) leads to a pressure increase of just a few percent. Note that it is critical for the temperatures to be converted to absolute units. If you had used Celsius temperatures, you would have predicted that the pressure should double, which is far greater than the actual increase. b) Nitrogen gas is introduced into a large deflated plastic bag. No gas is allowed to escape, but as more and more nitrogen is added, the bag inflates to accommodate it. The pressure of the gas within the bag remains at 1 atm and its temperature remains at room temperature (20 0 C). How many moles n have been introduced into the bag by the time its volume reaches 22.4 L? ( ) 5 3 3 1.013 10 22.4 10 0.932 8.3 / 293 PV Pa m PV nRT n mol RT J K mol K × = = = × One mole of gas occupies 22.4 L at STP (standard temperature and pressure: 0 0 C and 1 atm). This fact may be worth memorizing. In this problem, the temperature is slightly higher than STP, so the gas expands and 22.4 L can be filled by slightly less than 1 mol of gas. c) Some hydrogen gas is enclosed within a chamber being held at 200 0 C with a volume of 0.025 m 3 . The chamber is fitted with a movable piston. Initially, the pressure in the gas is 5 1.5 10 Pa (about 1.5 atm). The piston is slowly extracted until the pressure in the gas falls to 5 0.95 10 Pa .

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