Problem 1: idealised Lenoir heat engine cycle [15 marks] (a) Please explain what adiabatic process, isochoric...

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Problem 1: idealised Lenoir heat engine cycle [15 marks] (a) Please explain what "adiabatic process", "isochoric process" and "isobaric process" are. (b) In an idealised version of the Lenoir heat engine cycle, the gas which was originally having a temperature T₁, volume V₁ and pressure P₁ absorbs an amount of heat QH from a hot reservoir which is maintained at temperature T2, the heat absorption being an isochoric process and continuing until the gas has thermally equilibrated with the hot reservoir. At this point the pressure of the gas is P₂. The gas in the engine then undergoes an adiabatic expansion, reaching a volume V3 at which point the pressure of the gas is P₁. In the final step of the cycle, the gas releases heat of magnitude Qc into a cold reservoir (which has temperature 7₁), by undergoing an isobaric compression until it reaches its original equilibrium state T = T₁, V = V₁, P = P₁. Please draw the Lenoir cycle on a PV diagram. (c) Please calculate QH and Qc. (d) Please write down a relation between the temperatures and pressures of a pair of equilibrium states connected by an adiabatic process. (e) By assuming that the gas is an ideal gas which stays inside the engine (so the number of moles is constant), and making use of the relation you derived in part (d), please derive the efficiency of the idealised Lenoir cycle, expressing your answer in terms of only (which is the ratio Cp/Cy) and the temperatures of the hot and cold reservoirs. Problem 1: idealised Lenoir heat engine cycle [15 marks] (a) Please explain what "adiabatic process", "isochoric process" and "isobaric process" are. (b) In an idealised version of the Lenoir heat engine cycle, the gas which was originally having a temperature T₁, volume V₁ and pressure P₁ absorbs an amount of heat QH from a hot reservoir which is maintained at temperature T2, the heat absorption being an isochoric process and continuing until the gas has thermally equilibrated with the hot reservoir. At this point the pressure of the gas is P₂. The gas in the engine then undergoes an adiabatic expansion, reaching a volume V3 at which point the pressure of the gas is P₁. In the final step of the cycle, the gas releases heat of magnitude Qc into a cold reservoir (which has temperature 7₁), by undergoing an isobaric compression until it reaches its original equilibrium state T = T₁, V = V₁, P = P₁. Please draw the Lenoir cycle on a PV diagram. (c) Please calculate QH and Qc. (d) Please write down a relation between the temperatures and pressures of a pair of equilibrium states connected by an adiabatic process. (e) By assuming that the gas is an ideal gas which stays inside the engine (so the number of moles is constant), and making use of the relation you derived in part (d), please derive the efficiency of the idealised Lenoir cycle, expressing your answer in terms of only (which is the ratio Cp/Cy) and the temperatures of the hot and cold reservoirs.