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 x 10^5 Pa and a Temperature of 27 Degree celsius. The air is suddenly compressed, so that no thermal energy enters or leaves the gas, to a volume of 30cm^3. The pressure rises to 6.5 x 10^6 Pa.

Determine the Temperature of the gas after compression.

Answer 1

given that,

initial pressure (P1)=

initial volume(V1)= 540

initial temperature(T1)=27degress= 315.15K

AND

final pressure(p2)=Pa

the final volume(V2)=

Now, we have to find the final temperature(T2);

since there is no energy exchange between the air and the surrounding,hence the process is adiabatic;

therefore,we can apply the formula,

   (FOR AN ADIABATIC PROCESS) .............eq1

   (where is heat capacity ratio)

  

on further solving we get, ...........eq2

putting PV=NRT in eq1 we get,

HENCE,    (FOR AN ADIABATIC PROCESS)

.......eq3

from eq2 we know that , hence putting it in eq2 we get

HENCE THE TEMP OF THE GAS AFTER COMPRESSION IS   

HENCE T2 = 985.34 K