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Consider a Diesel cycle with air as a working substance. The cycle starts with an adiabatic compression of the air from a state a with a volume V3 to a state b with volume V₁. At the end of the compression, fuel is sprayed in and ignited, resulting in an isobaric expansion to state c with volume V₂ followed by an adiabatic expansion back to volume V3 (state d).Finally the exhaust is expelled, corresponding to an isochoric reduction of the pressure that completes the cycle and brings the air back to state a. i) Draw the Diesel cycle. Label the volumes V₁, V₂ and V3, and the states a, b, c and din a PV diagram. ii) Give an expression for the heat absorbed by the air when the fuel is ignited, Q₁, and the heat expelled, Q2, when the exhaust is expelled in terms of the temperature. iii) Find the ratio between the initial and final temperatures for (1) the adiabatic compression, and (2) the adiabatic expansion. Give your answers in terms of the expansion ratio r. and the compression ratio r. = ₁.=

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