Question

0.5 mole of a monatomic ideal gas is loaded into a cylinder and contained by a frictionless piston. The piston is set so that there is an initial volume of 2L. The gas in the cylinder is at a temperature of 298K. The gas is allowed to expand adiabatically against 1 atm of pressure. Calculate V/n initial, q per mole, w per mole, delta U per mole, delta S per mole and delta H per mole. What is the final temperature of the gas in Kelvin and Celcius?

Answer 1

moles n = 0.5

V = 2L

T = 298 K

P V = n RT

P x 2 = 0.5 x 0.0821 x 298

P = 6.12 atm

P1 = 6.12 atm

P2 = 1 atm

for monaoatomic gas = 1.66

P1 / P2 = (V2/V1)^

6.12 / 1 = (V2 / 2)^1.66

V2 = 5.96 L

(a) V/ n initial = 2 / 0.5 = 4 L /mol

(b) (V1/V2)^ ( -1) = (T2 / T1)

      (2 / 5.96) ^ (1.66 -1 ) = T2 / 298

T2 = 144.9K

final temperature =T2 = -128 ^oC

(c) w per mole

w =   (P1 V1 - P2 V2 ) / (-1)

w = ( 6.12 x 2 - 1 x 5.96 ) / (1.66-1)

w = 9.52 L -atm

w = 9.52 x 101.32 J

w= 964.4 J

for 1 mol

w = 964.4 /0.5 = 1928.8 J /mol

w = 1.929 kJ /mol

(d )   for adiabatic process   q = 0

(e) dU = q + w

       dU = w =

    dU = 1.929 kJ /mol

(f) dH = dU + n R dT

            = 1.929 + 0.5 x 8.314 x 10^-3 (144.9 -298)

            = 1.292 kJ/mol