Question

Problem 1) (40 pts) The French engineer, Guy Negre, invented an "eco-taxi," a low pollution vehicle to be built in Mexico beginning in the year 2001. Its energy storage system consists of compressed air tanks that, on demand, operate an engine (it could be a turbine, but in the case of this car, it is a piston device). There are several problems to be considered. Let us limit ourselves to the turn-around efficiency of the energy storage system. For comparison, consider that a lead-acid battery has a turrn around efficiency of somewhat over 70% and fly wheels, more than 90%. A very modern compressed gas canister can operate at 500 atmospheres. a) Calculate the energy necessary to compress 1 kilomole of air (γ-1.4) isothermally from 1 to 500 atmospheres. The temperature is 300 K b) One could achieve the same result by compressing the air adiabatically and then allowing it to cool back to 300 K. Calculate the energy necessary to accomplish this c) The compressed air (at 300 K) is used to drive a turbine (in the French scheme, a piston engine). Assume that the turbine is ideal-isentropic-and it delivers an amount of mechanical energy equal to the change of enthalpy the gas undergoes when expanding. How much energy does 1 kilomole of air deliver when expanding under such conditions? To solve this problem follow the steps suggested below. i. Write an equation for the change of enthalpy across the turbine as a function of the input temperature (300 K) and the unknown output temperature Using the polytropic law, find the output temperature as a function of the pressure ratio across the turbine. Assume that the output pressure is 1 atmosphere. If you do this correctly, you will find that the temperature at the exhaust of the turbine is below the liquefaction point of the gases that make up air. This would interfere with the turbine operation, but in the present problem, disregard this fact. ii. ii Once you have the exhaust temperature, calculate the mechanical energy generated by the turbine d) What is the turn-around efficiency of the compressed air energy storage system under the (optimistic) assumptions of this problem-that is, what is the ratio of the recovered energy to the one required to compress the air?

Answer 1

Sof:- n: t Kilomole 250o ałm T= 300 K W 5.5K lo6 J(-ve)

Adiabatic Compressian (T-T) ツー) o. 2857 300 (500) Ve

Looding to 3ook mx 1.oo5x (1衬1-3o) Ix 8.31 6.287 ท. 28.96 K (C TUr bine rM m- 28.16 ky i Tomole

0 given tht Process ACYOSSthe tubbine is So-tnopic 30o 500 56.818 k : 28.96 x 1.005 (30- 50.818) 52 39 K3 doptimestic (1o) 752.31 5.5x0 0 0.678 : 4678

ち Pdiabatic с. %252 . 39 x lo3+12.239メ166 30, 5구 4x1。6 : o. 6375