Question

5 holes of ideal gas expand isothermally and reversibly from a pressure of 10 atmosphere to 2 atmosphere at 300 Kelvin what is largest mass approximate which can be lifted through a height of 1 m in this expansion

Answer 1

Number of moles (n) = 5 moles
Initial pressure (P₁) = 10 atm
Final pressure (P₂) = 2 atm
Gas constant (R) = 8.314 J K^-1mol^-1
Temperature (T ) 300 K
Work done (W) = -2.303 nRT log (P₁ / P₂)
W = -2.303 X 5 X 8.314 X 300 log (10 / 2)
W = 28720.713 X log 5
W = 28720.713 X 0.698
W = 20047.057 J = 20.047 KJ
Now , work done = F x d
F = m g (g is negative as it is in opposite direction)
W = m g d
d = 1 m
m = W / g d
m = 20.047 / -9.8 1
m = 2.045 Kg