MASTERING PHYSICS PHY132 HW 16-1

MASTERING PHYSICS PHY132 HW 16-1 - HW16.1 Due 11:00pm on...

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HW16.1 Due: 11:00pm on Monday, October 11, 2010 Note: To understand how points are awarded, read your instructor's Grading Policy . [ Switch to Standard Assignment View] Introduction to the Ideal Gas Law Learning Goal: To understand the ideal gas law and be able to apply it to a wide variety of situations. The absolute temperature , volume , and pressure of a gas sample are related by the ideal gas law , which states that . Here is the number of moles in the gas sample and is a gas constant that applies to all gases. This empirical law describes gases well only if they are sufficiently dilute and at a sufficiently high temperature that they are not on the verge of condensing. In applying the ideal gas law, must be the absolute pressure, measured with respect to vacuum and not with respect to atmospheric pressure, and must be the absolute temperature, measured in kelvins (that is, with respect to absolute zero). If is in pascals and is in cubic meters, use . If is in atmospheres and is in liters, use instead. Part A A gas sample enclosed in a rigid metal container at room temperature (20 ) has an absolute pressure . The container is immersed in hot water until it warms to 40 . What is the new absolute pressure ? Hint A.1 How to approach the problem Hint not displayed Hint A.2 Convert temperatures to kelvins Hint not displayed Express your answer in terms of . ANSWER: = Correct 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. Part 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 [ Print ]
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remains at 1 and its temperature remains at room temperature (20 ). How many moles have been introduced into the bag by the time its volume reaches 22.4 ? Hint B.1 How to approach the problem Hint not displayed Express your answer in moles. ANSWER: = 0.932 Correct One mole of gas occupies 22.4 at STP (standard temperature and pressure: 0 and 1 ). This fact may be worth memorizing. In this problem, the temperature is slightly higher than STP, so the gas expands and 22.4 can be filled by slightly less than 1 of gas. Part C Some hydrogen gas is enclosed within a chamber being held at 200 with a volume of 0.025 . The chamber is fitted with a movable piston. Initially, the pressure in the gas is (about 1.5 ). The piston is slowly extracted until the pressure in the gas falls to . What is the final volume of the container? Assume that no gas escapes and that the temperature remains at 200 .
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