Physik für Biologen (129226)

Eine Metallkugel (punktförmig) mit der Masse m ist an einem Faden vernachlässigbarer Masse befestigt und bewegt sich horizontal mit konstanter Geschwindigkeit v auf einer Kreisbahn mit dem Radius R. Der Faden wird im Zentrum reibungsfrei durch ein Rohr senkrecht nach unten geführt. Die Zentrifugalkraft wird durch die Kraft F F kompensiert. Die Erdanziehungskraft ist zu vernachlässigen (m-Ikg, v=Ims, R=1m). a) Berechnen Sie die Kraft F. b) Ändert sich der Drehimpuls und/oder die Rotationsenergie, wenn man am Faden zieht? Begründen Sie Ihre Antwort! c) Berechnen Sie die Geschwindigkeit v2 bei einer Verkleinerung des Radius auf ¼ R! Welche Arbeit muss dazu verrichtet werden?

(c) Now consider a process changing the state of the gas from state (1) to state (2) along the red line over state A. First, the gas is expanded in an isobaric process to twice its volume at state A (what is the temperature TA at this state?). Then, the gas is cooled down in an isochoric process. Calculate the work performed by (or on) the gas and the heat added to (or removed from) the gas during these two processes. Compare the total work and heat during the red process from state (1) to (2) with the isothermal process. What happened to the internal energy during the red process?

 Figure 1: A p, V -diagram for an ideal gas, indicating points (1) and (2) on the black isotherm (where T = 300 K), and the points A and B reached by isobaric and isochoric processes from points (1) and (2). You will need the following information: 1. The internal energy U of an ideal gas depends only on its temperature. This entails in particular that U remains constant (dU = 0) during any isothermal process. 2. The heat added in an isochoric process is ∆Q = CV · (T2 − T1) and during an isobaric process ∆Q = Cp · (T2 − T1), where T1 is the initial and T2 the final temperature. It holds that Cp − CV = nR. Calculate numbers for a monatomic gas, for which CV = 3/2 nR. (a) Consider an ideal gas in state (1) as depicted in Fig. 1. The gas is in the volume 1 m^3 at pressure 1000 hPa=10^5 Pa. How many moles of gas are there? (b) Consider the isothermal expansion of the gas to twice its volume (state (2) with V = 2 m^3 and p = 0.5 × 10^5 Pa). How much work ∆W was performed by the gas and how much heat ∆Q was added? Where did the heat come from? 

Work and heat for an ideal gas 

Figure 1: A p, V -diagram for an ideal gas, indicating points (1) and (2) on the black isotherm (where T = 300 K), and the points A and B reached by isobaric and isochoric processes from points (1) and (2). You will need the following information: 1. The internal energy U of an ideal gas depends only on its temperature. This entails in particular that U remains constant (dU = 0) during any isothermal process. 2. The heat added in an isochoric process is ∆Q = CV · (T2 − T1) and during an isobaric process ∆Q = Cp · (T2 − T1), where T1 is the initial and T2 the final temperature. It holds that Cp − CV = nR. Calculate numbers for a monatomic gas, for which CV = 3/2 nR
 A)  consider a process changing the state of the gas from state (1) to state (2) along the red line over state A. First, the gas is expanded in an isobaric process to twice its volume at state A (what is the temperature TA at this state?). Then, the gas is cooled down in an isochoric process. Calculate the work performed by (or on) the gas and the heat added to (or removed from) the gas during these two processes. Compare the total work and heat during the red process from state (1) to (2) with the isothermal process. What happened to the internal energy during the red process?

Kann jemand die Grundlagen der Dynamik und Energie erklären?