Question

12. Two identical flasks, each of volume V, are connected through a tube controlled by a stopcock. The material of which this apparatus is constructed is a perfect thermal insulator. Initially 1 mole of a monoatomic real gas is confined to one flask at a temperature of 300K and other flask is empty. The stopcock is then opened. Assumed that the heat capacity at constant Volume is not constant, but dependent of temperature given by Cy = 5T over a certain temperature range, where b is constant. Also, the relation between constant a and b is given by a/b=0.7369. PV = RT + at?, where a is a constant. (a) What is the temperature of the gas after the final equilibrium has been reached? (b) For the real gas satisfying the same equation of state above (a), if the gas is expanded isothermally and reversibly from v to eV, what is the transferred heat to keep the temperature T during expansion? Obtain an expression in terms of temperature. (Make sure this is not the same apparatus with above (a).

Answer 1

du = dw+q Since the process is adiabatic q=0 du = dw au = (4), ar+ (au), av = Cydr + [7 (), -p av PV = RT + are (**), = 8 + 24T 7(), = FT + 2a7 [7 (?), - -] – RT + 2472_RT apa? (1 ), - ] = TE du = Cydt + FAV dW = -Pet.dV since it is a free expansion Pext = 0 dW = 0 Therefore du = Cydr + Tav=0 au = f*61 4T+" 13 av =0 = b[1380 + aTž {nv]" = 0 = b[ 73 – (300)21 +aTžin2 = 0 T _3002 20142 T2 = 210.997K

du = dw+q dV = -p.dV+ (4), ar+ (2), av = p.dv +9 (4), ar+(24) av + p.4V = 4= (4), av + pav 9 = 7* av + RT 7272 av since the process is isothermal dT = 0 = 2^r*in () +RTIn ()