0.5 litre of an ideal gas at a pressure of 20 atm expands to a final volume of 0.5 m ^(3). The process obeys the equation PV = a constant, (i) Find the value of this constant (ii) What is the final pressure ? And (iii) Find, the work done by the gas,

0.5 litre of an ideal gas at a pressure of 20 atm expands to a final v

1.	0.5 litre of an ideal gas at a pressure of 20 atm expands to a final volume of 0.5 m ^(3). The process obeys the equation PV = a constant, (i) Find the value of this constant (ii) What is the final pressure ? And (iii) Find, the work done by the gas,
Answer» SOLUTION :`V _(1) = 0.5` liter `= 0.5 xx 10 ^(-3) m ^(3)` ` P _(1) = 20 atm = 20 xx 101325 Pa` `V _(2) =- 0.5 m ^(3)` `P _(2) = ?` `PV = P _(1) V _(1) = P _(2) V _(2)` ` P _(1) V _(1) = 20 xx 101325 xx 0.5 x 10^(-3)` `P _(2) = ( P _(1) V _(1))/( V _(2)) = ( 20 xx 0.5 xx 10 ^(-3))/( 0.5)` `= 0. 020 atm` Work done `W = RT log _(e) "" (T _(2))/( V _(1))` But `RT = P _(1) V _(1) = P _(2) V _(2)` ` W = 2. 303 P _(1) V _(1) log _(10) "" (V _(2))/( V _(1))` ` 2. 303 xx 20 xx 101325 xx 0.5 xx 10^(-3) xx 0.5 xx 10 ^(-3) xx log _(10) " "(0.5)/( 0.5 xx 10 ^(-3))` `= 2. 33 xx 10 ^(6) J`