2) (25 points) Adiabatic gas cycle Consider the cyclic adiabatic compression and expansion of one mole of a monoatomic ideal gas (c = 3/2) at a temperature T, from an initial volume of V, to an intermediate compressed volume of v./2 and then back again to the final volume of V., so that V, V./2 V a) The gas is compressed and expanded reversibly. Give the total work done on the system Wtot, the change in system energy AU, the change in system temperature AT, and change in system entropy AS of the reversible cycle Vo Vo/2 Vo. (Hints: find only the total cyclic change from initial to final---the intermediate values are not required. Think, don't calculate! b) The gas is compressed irreversibly from an initial volume of V, and temperature T, to an intermediate volume of V./2 using a large constant external pressure Pext = Pbig and then expanded irreversibly back to the final volume V. against a smaller constant external pressure Pext = PSMALL Calculate the total work done on the system Wtat, the change in system energy AU, the change in system temperature AT, and change in system entropy As of the overall irreversible cycle V. V./2 V.. Give your answers in terms of the external pressure difference Ap = PBIG - PsMall, initial temperature T., and volume V. (plus any necessary physical constants). Assume that psig is large enough to be able to compress the gas as described. (Hint: this is somewhat more difficult that part a), but again note that only the overall cyclic changes are requested.] Useful (and useless) information: Gas constant: R - 5.314 Joules mol'K Speed of light: c= 3 x 10 m sec? Gravitational constant: g -9.8 meters/sec Distance to farthest observable object in universe= 13 billion light years Mass of a quarter: w-5.678 Heat capacity of water: C = 4.184 joules/g-C Density of water: d=1g/cm Heat capacity of ale: approximately the same as water 1 liter -2.11 pints 2) (25 points) Adiabatic gas cycle Consider the cyclic adiabatic compression and expansion of one mole of a monoatomic ideal gas (c = 3/2) at a temperature T, from an initial volume of V, to an intermediate compressed volume of v./2 and then back again to the final volume of V., so that V, V./2 V a) The gas is compressed and expanded reversibly. Give the total work done on the system Wtot, the change in system energy AU, the change in system temperature AT, and change in system entropy AS of the reversible cycle Vo Vo/2 Vo. (Hints: find only the total cyclic change from initial to final---the intermediate values are not required. Think, don't calculate! b) The gas is compressed irreversibly from an initial volume of V, and temperature T, to an intermediate volume of V./2 using a large constant external pressure Pext = Pbig and then expanded irreversibly back to the final volume V. against a smaller constant external pressure Pext = PSMALL Calculate the total work done on the system Wtat, the change in system energy AU, the change in system temperature AT, and change in system entropy As of the overall irreversible cycle V. V./2 V.. Give your answers in terms of the external pressure difference Ap = PBIG - PsMall, initial temperature T., and volume V. (plus any necessary physical constants). Assume that psig is large enough to be able to compress the gas as described. (Hint: this is somewhat more difficult that part a), but again note that only the overall cyclic changes are requested.] Useful (and useless) information: Gas constant: R - 5.314 Joules mol'K Speed of light: c= 3 x 10 m sec? Gravitational constant: g -9.8 meters/sec Distance to farthest observable object in universe= 13 billion light years Mass of a quarter: w-5.678 Heat capacity of water: C = 4.184 joules/g-C Density of water: d=1g/cm Heat capacity of ale: approximately the same as water 1 liter -2.11 pints