Question

A gas at 20°C and atmospheric pressure fills a cylinder. The gas is transferred to a new cylinder with four times the volume, after which the pressure is one-third the original pressure. What is the new temperature of the gas in °C?

Answer 1

Given

   gas in cylinder 1 is of

   at temperature T1 = 20 0C, P1 = 1atm, V1 = v

transfered to cylinder 2 of

   volume V2 = 4 V, p2 = 1/3 P1 = 1/3 atm, temperature T2 = ?

from ideal gas equation PV = nRT

       T = PV/nR

here the no of moles is same so

   T2/T1 = P1V1/P2V2
  
   T2 = (P*v*20) /((0.333 P)(4v)) 0C

   T2 = 15.0150 0C
   T2 = 15 0C
the new temperature of the gas is 15 0C