Question

2. In the first week of class, we encountered the following formula: where c is the specific heat of the substance. Now that we know a little more, we may see that the formula is ambiguous, since no particular process by which the temperature increases is specified. Let us explore this point a bit more carefully. a) Assum curves ("isotherms"). After determining which isotherm represents the lower temperature, label the colder isotherm temperature Ti and the warmer one T2. Thus, any process that starts on the first isotherm and ends on the second isotherm increases the temperature of the gas by Δ7-T2- Ti e you are working with an ideal gas. In a PV-diagram, draw two different isothermal b) In the diagram, sketch and label an isobaric process that achieves this temperature increase of ΔΤ. Assume the constant pressure is Pi, and that the volume changes from Vi to V2. c) Now sketch and label an isovolumetric process that also achieves this temperature increase of ΔT. Assume the constant volume is Vi, and that the pressure changes from Pi to P2. d) For both processes find the work done by the gas. Next, find AEint for both processes. Finally, find the two heat transfers, Q. Are the Q's the same for the two processes? You may leave all your answers in terms of the variables P1, P2, Vi, V2, Ti, T2, N, and ka. e) You should have found that the two Q's are different, depending on whether it was an isobaric or isovolumetric process. Just knowing the change in temperature is not enough to calculate how much heat was transferred! Therefore, in order to still use Eq. (1) above, we must define both a specific heat at constant volume, Cv, and a specific heat at constant pressure, Cp. Based on your answers, which one is larger?

Answer 1

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