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JZ_thermal_review - Some Review Problems and Solutions by...

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Some Review Problems and Solutions by Joel Zylberberg Here are some practice thermodynamics problems (and solutions). These are all tricky for one reason or another. So, if you can do all of these with ease, you are doing great! If there are some steps that are tricky, don’t be upset, but do try to understand where you have gone wrong. The problems are listed first, then I present the solutions. This way you can look at the problems and try them yourself without already having accidentally seen the solution. 1. Expansion, ideal gas A box (10cm on each side, with an open top) is at 273 K in a room full of N 2 gas at 1 atm pressure. The box has linear expansion coefficient α = 10 - 3 K - 1 . a) How many moles of N 2 are in the box? b) If I heat the room and the box to 373 K, what is the new box volume? c) At 373 K, how many moles of N 2 are in the box? d) in the heating process, how much did the total internal energy contained in the gas in the box change? 2. Mean free path and RMS speed In a room at 273 K, I have a bunch (100 per m 3 ) of N 2 atoms. a) What is their RMS speed? b) What is their mean free path (assume the molecules are spheres, radius r=10 - 10 m) c) On average, how many collisions/sec does each atom make? 3. Calorimetry and 2 nd law 1 kg of steam at 200 o C is placed in a box with 8 kg of ice at -20 o C. a) What is the final temperature of the mix? b) What is the change in entropy of the ice? (assume the volume of ice does not change much as it melts)? c) Using our statistical notion of entropy, what is the ratio of number of states initially available to the ice to the final number of states (w f /w i )? d) Considering only the ice (ignore the steam), which state is more probable (initial or final)? e) What do c), d) tell us in light of the 2 nd law? 4. Conduction, Carnot engines, and adiabatic processes A rod (with conductivity κ = 5 Jm - 1 s - 1 K - 1 ), which has rectangular cross-section 5 cm x 5 cm and length 1 m has one end in an oven at 300 o C. The other end is in a water bath at 100 o C. A Carnot engine operates between this bath of 100 o C water (as it’s heat reservoir), and a water bath at 0 o C (the cold reservoir). a) How much heat flows through the rod to the hot water bath? b) What is the efficiency of the (Carnot) engine? c) In 10 seconds, how much work is done by the engine? d) Assume that this 10 s of work is used to perform an adiabatic compression of a piston full of 1mol of N 2 gas.
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