A conducting and closed container of capacity 100 litre contains an ideal gas at a high pressure. Now using a pump, the gas is taken out at a constant rate of 5 litre s ⁻¹ . Find the time taken in which the pressure will decrease to P_ initial 100 . (Assume isothermal condition)

Step-by-step solution

The gas is taken out at the rate of 5 lit s ⁻¹ . The volume of gas ejected in ' d t ' time is d( vol )=5 d t Moles of gas ejected = n V (5 d t) aligned & P V=n R T (d p) V=(d n) R T & (d p) V=- ( n V 5 d t ) R T & (d P) V=-5 d t n R T V =-(5 d t) P & -d P P = 5 V d t d P P =- 5 100 d t=- 1 20 d t & _ p_i ^ p_f d P P =- 1 20 _ t=0 ^ t=t d t P_f=P_i e^ -t 20 & P_i 100 =P_i e^ -t 20 & t=20 100=92 sec . aligned