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110A oldmid

# 110A oldmid - (o M mdﬁrm 1 Consider a thermally isolated...

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Unformatted text preview: (o M mdﬁrm) 1. Consider a thermally isolated piston-cylinder arrangement containing a gas. Suppose the gas is allowed to expand reversibly from volume V1 and pressure p1 to volume V2 and pressure p2. Suppose further that an electric heater does work on the gas throughout the expansion such that the temperature of the gas remains constant at T. The Joule-Thomson coefﬁcient [1 of the gas can be determined from the total electrical work performed during the expansion. (a) (15 points) Show that p. is given by the following expression M = 01:09:1— P1) [W + /: Vdpl (1) gas (assumed to be constant) where C10 is the constant pressure heat capacity of the and we is the total electrical work performed. (Remember: (98%) T — ”Cp.) (b) (15 points) Make use of eqn. (1) to show that u = 0 for an ideal gas. (Remember: dU = 0 for the isothermal expansion of an ideal gas.) 2. (25 points) One gram of liquid benzene was burned in a constant-volume, adiabatic bomb calorimeter: C6H6(l) + 15/202(g) —>ﬁC02(g) +ngO(l) The temperature before ignition was 293.976 K and the temperature after ignition was 298.15 K. Take the constant-volume heat capacity of the calorimeter prior to the reaction to be 10,000 JK“. Calculate the enthalpy of formation of liquid benzene -— i.e., AH?(C6H5(1)) — at 298.15 K. (You may assume that AH? values are pressure independent and that all gases are ideal gases. You will need data from Tables 2.9 and 2.10 at the back of Atkins - starting on p. 938.) 3. (a) (10 points) Show for reactions involving ideal gases as reactants and products that the enthalpy change in the reaction at constant T is independent of pressure. (10 points) Calculate the standard enthalpy of vaporization of H200) at 320 K given that the corresponding value at 373.15 K — the boiling point of H200) — is 40.656 kJ—mol‘l. (You will need data from Table 2.10 of Atkins.) You may assume that any relevant heat capacities are temperature independent. (25 points) It can be shown that T‘ av T‘ 6T V p Consider an isothermal, reversible expansion of a van der Waals gas from volume V1 to volume V2 at temperature T. Show that the heat involved in the expansion is given by V2 - nb q = nRT an1 _ nb Recall that the van der Waals equation of state is nRT nza p=V-—nb- v2 Ail/074M 0A0 ”if/(efm 1. (a) (20 points) Show that the total differential of the enthalpy (H) of a closed system of . . . constant composxtion can be expressed in terms of volume and pressure as follows- where C}, is the constant pressure heat capacity, my E —(1/V) (5351) p is the Joule P ’ ' T Thompson coefficient, and o: E (1/V)(%Yf) . You may use the fact that dH : P -pdep + CPdT. (b) (15 points) Show that the total differential of the pressure of a closed system of constant composrtion can be expressed in terms of volume and temperature as follows: taw- t: 1w T cesses calculate the work w, heat q, and the changes '2. For each of the two following pro aki’ for a system consisting of 1.00 mol in internal energy U,xenthalpy H, = 4.0R (6,, is the Assume that H20 vapor is an ideal gas with 6', of H20 vapor. ). Assume C, is independent of constant pressure heat capacity per mole of H20(g temperature and pressure.) = 0.500 atm, V} =: 65.6 L, (a) (15 points) An adiabatic reversible compression from p. T‘ : 400 K, to a ﬁnal pressure pi = 1.00 atm. = 0.500 atm, 14 = 65.6 L, mal, reversible compression from p‘ (b) (15 points) An isother atm and V; = 32.8 L. T, = 400 K, to pf = 1.00 3. When nitroglycerine explodes, the chemical reaction that occurs can be assumed to be 5 3 1 CaHsNaosUl —* 3C02(9) + 5320(9) + 5N2(9) + 302(9) (10 points) Calculate the standard enthalpy and internal energy changes for the above reaction at 298 K given that the enthalpy of formation of liquid nitroglycerine at 298 K is —372.4 M mol—1. You may assume that all gases are ideal gases. (25 points) Consider 0.20 mol of nitroglycerine at 298 K and 1 bar, an amount which completely ﬁlls a constant-volume container of 0.03 L. This nitroglycerine explodes inside the container, and the cell and reaction products come to equilibrium. Cal- culate the ﬁnal temperature and pressure inside the constant-volume cell under the assumptions that the cell and its contents are thermally isolated from the surround— ings and that the contant—volume heat capacity of the cell plus reaction products has 7—1 the temperature independent value of 0.1 H I\ . Assume that all gases are ideal. (Hint: Some results from part (a) will be useful.) i i a 4 i i 3 3 i 2" Pi a '3 i 1‘: "1 . 1. A gas is held in place in a cylinder by a frictionless, massless piston, as shown in the figure at left below. The piston has a platform on top so that a mass M Ean be placed on it. The cross-sectional area of the piston and cylinder is 100 cm , the cylinder contains 0.100 moles of ideal gas, and initially, in absence of any mass M, the pigton is held in place by the pressure of the atmosphere, P m = 1.01 x 10 newtons m'2 (so that this must also be the SE inside the cylinder. For all parts of this problem except (f) on and cylinder to have a diabatic (diathermal) wall with temperatw (a) A mass M = 100 kg is placed on the platform. What is the new pressure of the ga§_after equilibrium is reached? Acceleration due to gravity = 9.8 m 5:1. (b) How far downward has the 100 kg mass dropped after equilibrium is reached? (c) How much work is done by the dropping mass on the gas: er of heat between the gas and its surroundings in the process as described? If so, how much, and in what direction? (e) 00 an of y0ur answers in parts (a)~(d) above depend upon whether the mass do any of your answers depend on whether fal s slowly or ra idl ? (I.e., the compression 0? the gas is reversible or not?) you have to bring the gas in the cylinder in order (i.e. to expand the piston of the process)? (d) Is there any net transf (f) To what temperature would to lift the mass back to its original position back out to where it was before the beginning ght below) is surrounded by an adiabatic wa 2. A thermodynamic system (sketched at ri and held at a constant pressure (no exchange of heat wit surroundings P = 10.0 atm = 1.01 x 10 newtons m' . Work is done on the system by an external Joule experiment. The motor motor, turning a paddle inside the system as in the provides 100 watts of power (1 watt = 1 Joule s‘ ) for 10.0 sec. At the conclusi of this process, the volume of the system has increased by 10.0 cm3 = 1.00 x 10-5 m3, and its temperature has increased from 300 K to 305 K. Calculate Op of the system, assuming Cp independent of temperature and volume. 100 kg PISTON (AREA 2 100 CM ) MOTOR . £¥~ P = 10.0 Figure for ' Fl ure for Problem l_ SYSTEM Prgblem 2 __..__—.——— « a.» "VIM.- ...
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110A oldmid - (o M mdﬁrm 1 Consider a thermally isolated...

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