One mole of an ideal gas is heated at constant pressure from 0oC to 200oC.
(a) Calculate work done.
(b) If the gas were expanded isothermally & reversibly at 0°C from 1 atm to some other pressure Pt, what must be the final pressure if the maximum work is equal to the work involved in (a).
(a) Work done:
Work done during heating of gas from 0oC to 200oC
Here,
T1 = 0oC = 273 K
T2 = 200oC = 473 K
Now
W = – PΔV = -P (V2 – V1)
= – P [(nRT2/P)-(nRT1/P)]
= – nR (T2–T1) = –1 × 1.987 × (473 – 273)
= – 397.4 cal
(b)If work equivalent to 397.4 cal is used for gas at 0oC, causing its isothermal expansion, from 1 atm to pressure Pt
As work done in reversible isothermal expansion is given by:
w = – 2.303nRTlog (P1 /P2)
-397.4 = – 2.303 × 1.987 × 273log (1/Pt)
Therefore, Pt = 1.272 atm
Hence, final pressure is 0.694 atm
