Question

The volume of some air, assumed to be an ideal gas, in the
cylinder of a car engine is 540cm^{3} at a pressure of 1.1
× 10^{5}Pa 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 cm^{3}. The pressure rises to 6.5 ×
10^{6}Pa.

Determine the temperature of the gas after the compression.

Answer #2

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

answered by: anonymous

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