CH353MHomework assignment 1 (due Wed Feb. 3)1. The beer and ice cream diet (To simplify calculations and avoid promoting an unhealthy lifestylebeer and ice cream are considered to be water and ice below).Nutritionists say that in order to consistently lose weight without much damage to our health onehas to spend an extra 200 kcal per day (note that the US “food calorie” is actually a kilocalorie.Correct units are used on food packages in Europe).a. Suppose you want to achieve this by drinking cold (8°C) water every day. Yourbody will have to burn extra calories in order to bring the temperature of waterup to the normal body temperature which is about 36.7°C. Calculate how muchwater one should drink per day in order to comply with this weight reductionplan.b. If you did Part a. you probably found out that the required daily amount of wateris a bit too large. Consider a diet in which one eats ice (at 0°C) instead. Use thefact that it takes 6.01 kJ to melt one mole of frozen water (you will learn moreabout melting later in the course). How much ice should one eat in order to spend200 kcal this way?2. Thermodynamics of weight lifting. Suppose that discouraged by the solution of Problem 1 you decided to take up weight training instead and that your idea of weight training is to lift a 200lbs barbell 100 times during your training session.a. Suppose also that each time the barbell is lifted ?h = 2 meters above the ground it isallowed to fall freely to the floor (not a recommended practice but will do as a physicalmodel). Calculate the total work W that is done by you on the barbell during the session.b. Suppose now that instead of dropping the barbell every time after you lift it you slowlylower it back to the floor. Calculate the total work W that is done by you on the barbell inthis case.c. Which training method a or b is more efficient as a way of “burning calories”? Why?d. Discuss what happened to the energy stored in the food you ate before going to the gymin cases (a) and (b)3.a. A bicycle tire contains air at P=8 bar (1 bar = 105 Pa). The volume of the tire is 0.0006m3. The temperature of air is 300K. Estimate the number of molecules of gas inside thetire.b. Calculate the work that you would have to perform to inflate the tire to the requiredpressure of 8 bar. Assume that the process is performed at a constant temperature equalto 300K. The atmospheric pressure is 1 bar and the air can be considered to be an idealgas.c. The constant temperature assumption that we have made in part b is not very realistic.Typically the air inside the tire and the pump gets hot as you inflate the tire. As adifferent approximation let us assume that there is no heat exchange between the air thatis being compressed and the surroundings. Calculate the amount of work one needs to do to perform reversible adiabatic compression of the same amount of air as in Part a fromP=1 bar to P=8 bar. The initial temperature of air is 300K. Assume cV = 5R / 2 for air.4. A balloon filled with hot air at T=400K is released at sea level. Estimate the elevation h of theballoon above sea level when it stops rising. The balloon is made from an elastic material suchthat the pressure inside and outside the balloon can be considered equal. The weight of theballoon material is also negligibly small. Assume that the heat exchange between the balloon andthe surroundings can be neglected. Assume that the temperature of the atmosphere is the same atall elevations and equal to Ta = 300K. The average molar mass of air is 29 g/mol and the molarheat capacity of air at constant volume is cV = 5R / 2 . Also assume that air is an ideal gas.5. Estimate the number of molecules in the Earth’s atmosphere. To solve this problem you willneed to come up with reasonable physical assumptions and use commonly available information(e.g. the atmospheric pressure composition of air size of the Earth etc.) Of course yourestimate would not be the exact answer but rather a crude order-of-magnitude estimate.6* (extra credit 15 points). A test tube of mass m = 10g filled with one mole of helium atT=300K is floating in vacuum in the absence of gravity. Initially the velocity of the test tube ismeasured to be zero. Estimate the velocity of the test tube after its cap (whose mass is negligible)is removed and all the helium atoms escape the test tube.1 mol of Hevacuumremove!
