3. 0.03 kg of air are adiabatically compressed in the cylinder of a diesel engine at the start of compression the volume of the cylinder filled with air is 0.03m^3 and the pressure at the end of compression is 3 .64 MPa. What will be the temperature of the air at the end of compres- sion if its volume decreases by a factor of 13.5 ?

To solve this problem, we can use the ideal gas law and the adiabatic compression equation.<br /><br />Given information:<br />- Initial volume of the cylinder filled with air, V1 = 0.03 m^3<br />- Final pressure at the end of compression, P2 = 3.64 MPa<br />- Volume decreases by a factor of 13.5, so the final volume, V2 = V1 / 13.5<br /><br />We need to find the final temperature of the air at the end of compression, T2.<br /><br />The ideal gas law states that the product of pressure and volume is proportional to the temperature, which can be written as:<br /><br />P1V1/T1 = P2V2/T2<br /><br />Since the process is adiabatic, there is no heat transfer, and the specific heat ratio (γ) remains constant. The adiabatic compression equation can be written as:<br /><br />P1V1^(γ) = P2V2^(γ)<br /><br />Substituting the given values and solving for T2, we get:<br /><br />T2 = (P2 * V2^(γ)) / (P1 * V1^(γ))<br /><br />T2 = (3.64 MPa * (0.03 m^3 / 13.5)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa00222 m)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T2 = (3.64 MPa * (0.00222 m^3)^(γ)) / (1 MPa * (0.03 m^3)^(γ))<br /><br />T