Question

10 moles of an ideal gas expand isothermally pressure of 5 atm to and reversibly from a 1 atm at 300 K. What is the largest mass that can be lifted through a height of 1 m by this expansion?

Answer 1

Given,

N = 10 moles

P_i = 5 atm

P_f = 1 atm

T = 300K

R = 8.134 J K^-1 mol^-1

H = 1m

\(\because\) W_exp = −2.303 nRT log\(\frac{P_i}{P_f}\)

= −2.303 × 10 × 8.314 × 300 log\(\frac{5}{1}\)

= −40.15 × 10³ J

If mass (M) can be lifted by this work through a height of 1m, then

Work done = Mgh

or M = \(\frac{Work\,done}{g\,h}\)

= \(\frac{40.15\times10^3\,kgm^2s^{-2}}{9.81\,ms^{-2}\times1m}\) [\(\because\) J = kg m²s^-2]

= 4092.76 kg