Awater bottle has a internal cross section of 5.000 x10-3 m2 (50.00 cm2 ) and a height of 0.2000 m (20.00 cm). it has a straw extending from 0.04 m above the top, to the very bottom of the bottle (24.00 cm total), which has a cross sectional area of 1.000 x 10-6 m2 (1.000 cm2 ). suppose you had the water bottle, partially filled with water, in the refrigerator to cool to a temperature of 275.0 k. when you remove the water bottle from the refrigerator, you seal the lid tightly, setting the initial pressure of the gas at the top of the bottle at 1 atm (101,300 pa). you note that the bottle, and the straw, are both filled to the same level, 16.00 cm above the bottom of the bottle.
i. [3 pts] draw a picture of the situation, label all the relevant dimensions.
ii. [4 pts] determine the number of moles of gas in the pocket of air trapped at the top of the water bottle.
iii. [6 pts] as the water bottle warms up, the gas at the top of the bottle expands, pushing water up the straw. determine the temperature of the gas when the water gets pushed to the very top of the straw. (hints: neglect any thermal expansion of the water or the bottle. only consider changes in temperature, pressure, and volume of the gas. find the volume of the gas first. will the pressure remain constant? )