The volume of some air, assumed to be an ideal gas, in the cylinder of a car engine is 540cm3 at a pressure of 1.1 × 105Pa and a temperature of 27 °C. The air is suddenly compressed, so that no thermal energy enters or leaves the gas, to a volume of 30 cm3. The pressure rises to 6.5 × 106Pa.
Determine the temperature of the gas after the compression.
Since the air is suddenly compressed, so that no thermal energy enters or leaves the gas the process is adiabatic.
Equation of adiabatic process is TV-1 =a constant.
where T= temperature of gas V=volume of gas
hence T1V1-1 = T2V2-1 .......................(1) where
T1= initial temperature of gas=270C=27+273=300K
V1=initial volume of gas=540cm3
T2= final temperature of gas =?
V2=final volume of gas=30cm3
= ratio of specific heat (Cp/Cv)=1.4 [for air]
eq(1) becomes
300x5401.4-1 = T2x301.4-1
300x540.4 = T2x30.4
T2=300x540.4 /30.4 =300x(540 /30).4
=300x18.4 =300x3.178=953K
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