Assignment 1 Soln

Department of Chemical and Biochemical Engineering CBE2224: Chemical Engineering Thermodynamics Assignment 1: Review Problems (Due Friday January 30, 2009: Locker # 420)

Problem 1: Two large gas storage spheres (0.1 m 3) each contain air at 2 bar (Figure below). They are connected across a small reversible compressor. The tanks, connecting lines, and the compressor are immersed in a constant temperature bath at 280 K. The compressor will take suction from one sphere, compress the gas, and discharge to the other sphere. Heat transfer between the bath and the tanks, lines and compressor is excellent. Assume that air is an ideal gas with C  p = 29.30 J/mol K.

(a) (b)

What is the work requirement to compress the gas in one sphere to 3 bar? What is the heat interaction with the constant-temperature constant-temperat ure bath?

Solution (Method 1):To 1): To begin with, let us consider tank A is our system. Then according to the problem, the compressor is taking gas from tank B and discharges it to tank A, isothermally (the problem states that the heat transfer is excellent). The work of the compressor from the analysis of  energy balance for open system will give: W Rev 

Because the gas is ideal, V  



P A

P B

VdP

nRT 

. Since we can not assume 1 mole, we want to know how the number P of moles change from one Tank to the other. If we look at the entire system, whatever leaves Tank A gets into Tank B. dn  dn A   dnB But we are told that the volume of the two tanks is the same. dn 

V

dP A  RT

V 

dP B dP A dP dP B RT