Question

One mole of an ideal gas expands reversibly and isothermally from 10. bar to 1.0 bar at 298.15K.

(i)Calculate the values of w, q, ∆U and ∆H?

(ii)Calculate w if the gas were to have expanded to the same final state against a constant pressure of 1 bar.

Answer 1

i) a)For isothermal process

temperature Change, ∆T =0

Therefore,

Internal Energy change , ∆U = 0

b) For isothermal expansion

work done , w = -nRTln(P1/P2)

= 1mol× 8.314(J/K mol) × 298.15K × 2.303log(10bar/1bar)

= -5708.7J

c) According to first law of thermodynamics ( IUPAC convention)

∆U = Q + w

∆U = 0

Therefore,

Q + w =0

Q= -w

therfore,

Heat added to the system, Q = -(-5708.7J) = 5708.7J

d) H = U + pv

pV = nRT

H = U + nRT

U + nRT is constant

Therefore,

Enthalphy change , ∆H = 0

¡¡) work done, w = - work done by system

= - (-5708.7J)

= 5708.7J