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Exhaling air out of our lungs costs us energy in the form of work, ~16 times per minute (maybe more during chemistry examinations!). a. Take a breath. Calculate the work required to exhale 0.50 L (the "tidal volume" or resting single breath volume of an average human) of air at approximately sea level, in units of J. Use appropriate significant figures. b. Assuming one takes 23,000 breaths per day, on average, how many doughnuts per day can one consume to meet this energy demand (assuming one doughnut imparts 300 Calories or 300 kcal of useful energy, and there is no energy cost for inhalation)? 2. Let us investigate the reversible isothermal compression of P* a pure gas in a closed, piston-like system from Vi to Vs a. Write a relevant expression of the First Law of Thermodynamics that we can use as a starting point Tüxed in determining the heat, work, and internal energy change during this process. AV=V1-Vi b. Write in the correct (in)equality symbol for each (choices: >,2,=,S,<,7): 4V. 4T AU W Bonus Point: 9 *Important: DO NOT assume any specific equation of state in parts a or b! C. Write the total differential of the internal energy, dU, of the system (the pure gas) in terms of T and V. d. If the gas is accurately described by a Berthelot equation of state (having Berthelot constants a and b), the expression for the change in internal energy upon reversible isothermal compression turns out to be: 2an2 1 Is this expression consistent with the result for an ideal gas? Use two methods (i.e., two different mathematical limits) to back up your claim. 3. Oxyacetylene welding is the most common gas welding technique, mainly owing to its high temperature flame. Acetylene (C2H2) is combusted in the presence of oxygen to produce carbon dioxide and steam, and the standard state combustion enthalpy of C2H2(g) at 298 K is - 1299 k] mol-1. CP (2981 K) Species (J K-¹ mol-¹ O2(g) 31.192 CO2(g) 46.882 H2O(g) 33.580 C2H2(g) 37.904 N2(g) 29.994 a. Calculate the maximum final temperature reached upon the combustion of acetylene in air (assumed to be 80% N2(g) and 20% O2(&)) at standard pressure and an initial temperature of 298 K. b. Most commonly, a supply of pure oxygen is provided to the welding torch along with the acetylene (instead of air). Comment on the expected maximum final temperature reached upon the combustion of acetylene in pure oxygen at standard pressure. Will it be higher, lower, or the same? S. Determine the standard state enthalpy of the following reaction at 298 K: CaC2 (s)+2H2O(1) Ca(OH)2 (s) + C2H2(g) Use the following data at 298 K: i. Ca(OH)2 (s) A°H = -66.5 k] ii. Formation enthalpy of CaO (s) A°H = -635.1 k) iii. Formation enthalpy of CaC2 (s) A°H = -62.81 kJ iv. Combustion enthalpy of C(graphite) A°H = -393.5 kJ VA Combustion enthalpy of C2H2 (g) A°H = - 1230 kJ * (to H2O (n) 6. Draw the experimental diagrama of the following two famous early thermodynamics experiments, and give il mathomatical explanation equations) for which major variable of state (with unito of is held constant in each: a Joule expansion ("free adiabatie" expansion) b. Joute/Thomson expansion ("isenthalpie" expansion) *If you cannot remember the specific experiments, draw a diagram for any one "free adiabatie" and any one "isenthalpie" expansion Diagram (a) Diagram (b) Mathematical Explanation (a) Mathematical Explanation (b) 7. It's 7am on Saturday morning, which means that it's time to bang out the weekend chores, bright and early. Your dad barks the usual orders: "Hey Sport! Wake up and compress that ideal gas, ASAP!" Not again. The family's ideal gas storage tank (3.00 L in volume) is held at 1.25 bar and 298 K. You have two choices: a two-step isothermal compression (the first step at a constant pressure of P=2.25 bar down to 1.00 L. and the second step at a constant pressure of P=4 bar down to the final volume of 0.50 L) OR a single, reversible isothermal compression all the way to 0.50 L. The second process takes more time, but is only a single step. However, as a lazy teenager, you always want to do the least amount of work. Which method requires the least amount of work? Calculate the work required for that method. If you need to, calculate both and select the method with less work.

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