n moles of an ideal gas with adiabatic index y = 2 is taken through a cycle as shown in the figure to the right, which is not necessarily drawn to scale. 4 The cycle proceeds as follows: 1-2 is an isobaric compression to V2 = Vo/2 2 – 3 is an isochoric process with P3 = 3P, 3 – 4 is an isothermal compression to V4 = Vo/4 4 – 5 is an isochoric heating process 5 – 1 is an adiabatic expansion back to Vo 3Po Po 2 Vo/4 Vo/2 Vo 3) What are Cv, the molar specific heat at constant volume, and Cp, the molar specific heat (a) at constant pressure, for this gas? Your answer should be in terms of n, R, To, or a subset of these quantities. (b) ( diagram) in terms of Po, and the temperatures T2, T3 , T4, and T3 (the temperatures at points 2 – 5) in terms of To. All work must be shown. Find the unknown quantities P4 and Ps (which are the pressures at points 4 and 5 on the Find the work done on the system in terms of n, R, T,, and pure numbers only for the (c) processes 1 → 2, 2 → 3, 3 → 4, 4 → 5, and 5 → 1. Make sure to show all your work and clearly label the work for each of the processes. (d) only for the processes 1 → clearly label the Q for each of the processes. Find the energy added to the system by heat (Q) in terms of n, R, T,, and pure numbers 2, 2 → 3, 3 → 4, 4 → 5, and 5 → 1. Make sure to show all your work and

n moles of an ideal gas with adiabatic index y = 2 is taken through a cycle as shown in the figure to the right, which is not necessarily drawn to scale. 4 The cycle proceeds as follows: 1-2 is an isobaric compression to V2 = Vo/2 2 – 3 is an isochoric process with P3 = 3P, 3 – 4 is an isothermal compression to V4 = Vo/4 4 – 5 is an isochoric heating process 5 – 1 is an adiabatic expansion back to Vo 3Po Po 2 Vo/4 Vo/2 Vo 3) What are Cv, the molar specific heat at constant volume, and Cp, the molar specific heat (a) at constant pressure, for this gas? Your answer should be in terms of n, R, To, or a subset of these quantities. (b) ( diagram) in terms of Po, and the temperatures T2, T3 , T4, and T3 (the temperatures at points 2 – 5) in terms of To. All work must be shown. Find the unknown quantities P4 and Ps (which are the pressures at points 4 and 5 on the Find the work done on the system in terms of n, R, T,, and pure numbers only for the (c) processes 1 → 2, 2 → 3, 3 → 4, 4 → 5, and 5 → 1. Make sure to show all your work and clearly label the work for each of the processes. (d) only for the processes 1 → clearly label the Q for each of the processes. Find the energy added to the system by heat (Q) in terms of n, R, T,, and pure numbers 2, 2 → 3, 3 → 4, 4 → 5, and 5 → 1. Make sure to show all your work and

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