Question

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

Answer 1

Work done in this case is given by  

$w\quad =\quad -nRT\quad ln\left( \frac { { P }_{ 1 } }{ { P }_{ 2 } }  \right)$

From the given,

Number of moles, n = 10

$R\quad =\quad 8.314\quad J{ K }^{ -1 }{ mol }^{ -1 }$

T = 300 K

Initial pressure ${ P }_{ 1 }$ = 10 atm

Final pressure ${ P }_{ 2 }$ = 2 atm

Substitute the given values  

$=\quad 10\quad mol\quad \times \quad 8.314\quad J{ K }^{ -1 }{ mol }^{ -1 }\quad \times \quad 300K\quad ln\left( \frac { 10\quad atm }{ 2\quad atm }  \right) \\ \\=\quad -40.15\quad \times \quad { 10 }^{ 3 }J$

Let M be the mass which can be lifted through a height of 1 m

Work done in lifting the mass = $M \times g \times h$

$w\quad =\quad M\quad \times \quad 9.81\quad { ms }^{ -2 }\quad \times \quad 1\quad m\\ \\M\quad \times \quad 9.81\quad { ms }^{ -2 }\quad \times \quad 1\quad { m }^{ 2 }{ s }^{ -2 }\quad =\quad 40.15\quad \times { \quad 10 }^{ 3 }J\\ \\M\quad \quad =\quad 409.\quad 29\quad kg$