The volume of a monatomic ideal gas doubles in an adiabatic expansion. (a) By wh

Question

The volume of a monatomic ideal gas doubles in an adiabatic expansion. (a) By what factor does the pressurechange?
1
(b) By what factor does the (Kelvin) temperature change?
2
(c) Verify your answers to parts (a) and (b) by considering171 moles of gas with an initial pressureof 330 kPa and an initial volume of 1.2 m3.
Find the pressure and temperature of the gas after it expandsadiabatically to a volume of 2.4m3.
Pf
3 kPa
Tf
4 K
pressure change factor in this case
5
temperature change factor in this case
6 (a) By what factor does the pressurechange?
1
(b) By what factor does the (Kelvin) temperature change?
2
(c) Verify your answers to parts (a) and (b) by considering171 moles of gas with an initial pressureof 330 kPa and an initial volume of 1.2 m3.
Find the pressure and temperature of the gas after it expandsadiabatically to a volume of 2.4m3.
Pf
3 kPa
Tf
4 K
pressure change factor in this case
5
temperature change factor in this case
6

Explanation / Answer

from the problem Vf =2Vi for mono atomic gas = 5/3 from the adiabatic exanpansion eq = PiVi = Pf Vf          (Pf/Pi ) = (Vi/Vf) substitue values we get = 0.315 (b) let Ti, Tf be thetemperratures    Tf/Ti =Pf/Pi * 2Vi/Vi            = 0.315 * 2 = 0.63    number of moles of gas = n = 175 moles intial presures Pi = 330 kpa intial volume of gas Vi = 1.2m3 final preasure Pf = Pi(Vi/Vf)                        = 330 ( 1.2/2*1.2 ) 5/3                         = 104 kpa now Pf/ Pi = 104/330 = 0.315 since Ti = PiVi/nR               = plug values we get Ti value ----K final temperature Tf =(Pf/pi ) ( Vf/Vi)Ti plug values we get Tf ------K    dfividing Tf/Ti giveschange in temparature plug values we get Tf ------K    dfividing Tf/Ti giveschange in temparature

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