Question

# The volume of some air, assumed to be an ideal gas, in the cylinder of a...

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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