Conceptual Questions: These questions are to be answered with a short para- graph. Problem 1. An ideal gas undergoes an adiabatic process. Choose ALL the true statements: (a) The temperature stays constant. (b) The entropy stays constant. (c) The work done by / on the gas is zero. ((1) The internal energy of the gas stays constant. (e) The heat transfer to / from the gas is zero. Problem 2. Biological systems (eg. living organisms) are highly ordered systems. The development of a living organism or the evolution of species from simpler to more complex ones is accompanied by a decrease of the entropy or the organism or species. Doesn't this violate the second law of thermodynamics? Explain. Complete Solution Questions: These problems are to be answered with detailed calculations. Problem 3. An ideal diatomic gas undergoes the increases in pressure and volume shown on the graph in Fig. l. The initial temperature of the gas is 297 K. Calculate: (a) the work done by the gas. (b) the temperature of the gas at the end of the process. (c) the change in internal energy in this process. ((1) the quantity of heat added to or removed from the gas in this process. 250 200 150 f 100 50 (l 0 l 2 3 4 5 Volume (1113) Pressure (Pa) Figure l: PV-Diagram. Problem 4. A heat engine is based on a cycle consisting of an isobaric, an isometri'. and an adiabatic process (Fig. 2). The working substance is 1.00 mol of ideal monatomic gas. The work done on the gas during the adiabatic process is 1023.3 J. (a) Find the work done by the gas for the entire cycle. (1)) Find the amount of heat for each process. (c) Find the efficiency of the heat engine. ((1) Find the internal energy at points 1 and 2. P, kPa 240 12.0 18.0 V. L Figure 2: One mole of ideal monatomic gas in a heat engine cycle. Problem 5. You are designing a Carnot engine that has 2 moi of ideal diatomic gas as its working substance. The gas is to have maximum temperature of 527\"C' and a maximum pressure of 5.00 (1.15m. W'ith a heat input of 400 J per cycle, you want 300 J of useful work. (a) Find the temperature of the cold reservoir. (1)) For how many cycles must this engine run to melt cmnpletely a 10.0kg block of ice, originally at 0.0%? using only heat rc-zjected by the engine? Exam Preparation Questions Extra Problem 1. A balloon holding 5.00mol of helium gas absorbs 925 J of thermal energy while doing 371 J of work expanding to a larger volume. (a) Find the change in the balloon's internal energy (1)) Calculate the change in the temperature of the gas. Extra Problem 2. A heat engine cycle consist of two isobaric processes (at pressures P and 2P) and two isometric processes (at volumes V and 2V); the cycle looks like a rectangle on the PV diagram. (a) Draw the cycle on a PV diagram. (b) Find the total work done on the gas for the cycle. Extra Problem 3. One mole of ideal monatomic gas undergoes the cycle shown in Fig. 3, consisting of an isothermal process AB at temperature 400 K, an isobaric process BC, and an isometric process CA (between pressures of 100 kPa and 200 kPa). The work done by the gas during the isothermal process is 2305 J. (a) Find the volumes VA = Vo and VB, and the temperature To. (b) Find the work done for the entire cycle. (c) Find the amounts of heat for each of the three processes. (d) Find the efficiency of this heat engine. P, kPa 1 A 200 T = 400 K 100 C B V , L Figure 3: One mole of ideal monatomic gas in a cycle