Course PHYSICS260 Assignment 5 Consider ten grams of nitrogen gas at an initial pressure of 6 0 atm and at room temperature It undergoes an isobaric expansion resulting in a quadrupling of its volume i After this expansion what is the gas volume ii Determine the gas temperature after this step In the next process the gas pressure is decreased at constant volume until the original temperature is reached iii After this decrease in gas pressure what is the value of the pressure In the final process the gas is retured to its initial volume by isothermally compressing it iv Determine the final gas pressure v Using appropriate scales on both axes show the full three step process on a p V diagram Introduction to the Ideal Gas Law Description Practice using the ideal gas law with a series of questions in which all but two gas parameters are held fixed Learning Goal To understand the ideal gas law and be able to apply it to a wide variety of situations The absolute temperature volume the ideal gas law which states that and pressure of a gas sample are related by 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 is in liters use If is in atmospheres and 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 Part A 1 How to approach the problem To find the final pressure you must first determine which quantities in the ideal gas law remain constant in the given situation Note that is always a constant Determine which of the other four quantities are constant for the process described in this part Check all that apply ANSWER so that and Now manipulate the ideal gas law this situation are isolated on the right side of the equation the constants in Since the right side of the equation is a constant in this situation the quantity which is always equal to must be the same at the beginning and the end of the process Therefore set then solve for the final pressure Plug in the values given in this part and Part A 2 Convert temperatures to kelvins To apply the ideal gas law all temperatures must be in absolute units i e in kelvins What is the initial temperature ANSWER 0 in kelvins 20 100 273 293 The Celsius and Kelvin temperature scales have the same unit size so to convert from degrees Celsius to kelvins just add 273 Express your answer in terms of ANSWER 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 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 Rearrange the ideal gas law to isolate Be sure to use the value for in units that are consistent with the rest of the problem and hence will cancel out to leave moles at the end Express your answer in moles ANSWER One mole of gas occupies 22 4 at STP standard temperature and pressure 0 and This fact may be worth memorizing In this problem the temperature is 1 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 of 0 025 with a volume The chamber is fitted with a movable piston Initially the pressure in the gas is about 1 5 in the gas falls to The piston is slowly extracted until the pressure What is the final volume of the container Assume that no gas escapes and that the temperature remains at 200 Part C 1 How to approach the problem To find the final volume you must first determine which quantities in the ideal gas law remain constant in the given situation Note that is always a constant Determine which of the other four quantities are constant for the process described in this part Check all that apply ANSWER Now look at the ideal gas law situation the quantity Since and which is always equal to beginning and the end of the process Therefore set are all constants in this must be the same at the Plug in the values given in this part and then solve for the final volume Enter your answer numerically in cubic meters ANSWER Notice how is not needed to answer this problem and neither is although you do make use of the fact that is a constant Part D Some hydrogen gas is enclosed within a chamber being held at 200 whose volume about 15 The is 0 025 Initially the pressure in the gas is chamber is removed from the heat source and allowed to cool until the pressure in the gas falls to At what temperature Part D 1 How to approach the problem does this occur To find the final temperature you must first determine which quantities in the ideal gas law remain constant in the given situation Note that is always a constant Determine which of the other four quantities are constant for the process described in this part Check all that apply ANSWER Now manipulate the ideal gas law so that and this situation are isolated on the right side of the equation the constants in Since the right side of the equation is a constant in this part the quantity which is always equal to must be the same at the beginning and the end of the process Therefore set Plug in the values given in this part and then solve for the final temperature Enter your answer in degrees Celsius ANSWER This final temperature happens to be close to room temperature Hydrogen remains a gas to temperatures well below that but if this question had been about water vapor for example the gas would have condensed to liquid water at 100 law would no longer have applied
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