The volume of a monatomic ideal gas doubles in an adiabatic expansion.
Considering 115 moles of gas with an initial pressure of 350 kPa and an initial volume of 1.4 m3 . Find the pressure of the gas after it expands adiabatically to a volume of 2.8 m3 .
Pf= 110 kPa
Find the temperature of the gas after it expands adiabatically to a volume of 2.8 m3 .
Number of moles n = 115 moles
Ratio of specific heat of monoatomic gas = 5/3
initial pressure P= 350 kPa 350000 Pa
initial volume V = 1.4 m3
Final pressure P ' = ?
Final volume V = 2.8 m3 .
In adiabatic process , PV = P ' V '
From this P ' = P ( V / V ' )
= 350 kPa (1.4/2.8) 5/3
= 350 kPa (0.3149)
= 110.24 kPa
(b). Initial tempearture T = PV / nR
= (350000)(1.4) /(115)(8.314)
= 512.49 K
In adiabatic process TV-1 = TV-1
From this final temperature T ' = T (V/V ') -1
= 512.49 (1.4/2.8) 2/3
= 322.85 K
Pf= 110 kPa
Find the temperature of the gas after it expands adiabatically to a volume of 2.8 m3
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