In a tyre of "Ferrari" car of Mr. Obama, a tube having a volume of 12.3 litres is filled with air at a pressure of 4 atm at 300 K.Due to travelling, the temperature of the tube and air inside it raised to 360 K and pressure reduced to 3.6 atm in 20 minutes. If the porosity (number of pores per unit area) of the tube material is `5xx10^3` pores/`cm^2` and each pore can transfer air from inside to outside of the tube with the rate of `6.023xx10^8` molecules per minute.Calculate the total surface area `(m^2)` of the tube.(R=0.082 Lt-atm/mole-K)
Give your answer divide by 100.

Answer

50

Explanation

Initial moles of air inside the tube `=(4xx12.3)/(0.082xx300)=2`
moles of air after 20 minutes`=(3.6xx12.3)/(0.082xx360)=1.5`
`:.` moles of air leaked in 20 minutes =2-1.5=0.5
`:.` molecules of air leaked in 20 minutes `=0.5 N_A`
Let the total surface area of tube =`A cm^2`
Total molecules escaped in 20 minutes`=(5xx10^6)A xx 6.023xx10^(8)xx20=0.5 N_A`
`:. A=(0.5xx6.023xx10^23)/(5xx10^5xx6.023xx10^8xx20)=5xx10^7 cm^2 =5000 m^2`