The working principle of combustion engines in many cars is called the Otto cycle. A mixture...

Transcribed Image Text:

The working principle of combustion engines in many cars is called the Otto cycle. A mixture of air with fuel is assumed to be the working substance. As a simplification, this mixture is assumed to be a perfect gas. The thermodynamic cycle consists of the following steps: 1) reversible adiabatic compression from A to B. 2) reversible pressure increase at constant-volume from B to C due to combustion of a small amount of fuel. 3) reversible adiabatic expansion from C to D. 4) reversible pressure decrease at constant volume from D to A. The perfect gas can has molar heat capacities Cp,m=7/2 R and Cp,m-Cv,m=R. The state A is described by: VA-6 dm³, PA-100 kPa, TA-300 K. The compression ratio is VA/VB-12 and the pressure increase is pc/PB=2. Hint: For adiabatic changes in a perfect gas: V 1-(7) = Vf ₂C=Cv.m/R V,m a) Sketch this thermodynamic cycle in a p-V diagram. Indicate, where heat flows and the direction of heat flow. (3pt) b) Show, that TB-810.6 K, Tc-1621.2 K and Tp=600 K. (4pt) c) Determine AU, q, w and ASsys for every step. (4pt) d) Calculate the efficiency of the cycle. (4pt) The working principle of combustion engines in many cars is called the Otto cycle. A mixture of air with fuel is assumed to be the working substance. As a simplification, this mixture is assumed to be a perfect gas. The thermodynamic cycle consists of the following steps: 1) reversible adiabatic compression from A to B. 2) reversible pressure increase at constant-volume from B to C due to combustion of a small amount of fuel. 3) reversible adiabatic expansion from C to D. 4) reversible pressure decrease at constant volume from D to A. The perfect gas can has molar heat capacities Cp,m=7/2 R and Cp,m-Cv,m=R. The state A is described by: VA-6 dm³, PA-100 kPa, TA-300 K. The compression ratio is VA/VB-12 and the pressure increase is pc/PB=2. Hint: For adiabatic changes in a perfect gas: V 1-(7) = Vf ₂C=Cv.m/R V,m a) Sketch this thermodynamic cycle in a p-V diagram. Indicate, where heat flows and the direction of heat flow. (3pt) b) Show, that TB-810.6 K, Tc-1621.2 K and Tp=600 K. (4pt) c) Determine AU, q, w and ASsys for every step. (4pt) d) Calculate the efficiency of the cycle. (4pt)

Answer rating: 100% (QA)

The detailed ... View the full answer