W3.F (template) - Thermo equilibrium, Ideal gas Thursday, January 22, 2015 5:41 PM Which system has the largest average translational kinetic energy per molecule? (assume rotational and vibrational effects are negligible) 1. 2. 3. 4. 5. 2 mol of He at p = 2 atm, T = 300 K 2 mol of N2 at p = 0.5 atm, T = 450 K 1 mol of He at p = 1 atm, T = 300 K 1 mol of N2 at p = 0.5 atm, T = 600 K 1 mol of Ar at p = 0.5 atm, T = 450 K Example: A paddle wheel frictionally adds thermal energy to 5.0 moles of an ideal monatomic gas in a sealed isolated container. The paddle wheel is driven by a cord connected to a falling object as shown in the figure. If all the loos of gravitational potential energy from the object goes into the thermal energy of the gas, how far has the 2.0-kg object fallen when the temperature of the gas increases by 10 k? (Answer 31.8 m) New Section 1 Page 1 You have two containers in contact with each other. One is full of helium gas. The other holds a larger number of nitrogen gas molecules. Both gases are in equilibrium with each other. How does the temperature of the helium compare to the temperature of the nitrogen? 1. THe>TN 2. THe<TN 3. THe=TN You have two containers in contact with each other. One is full of helium gas. The other holds a larger number of nitrogen gas molecules. Both gases are in equilibrium with each other. How does the total internal energy of the helium compare to the total internal energy of the nitrogen? 1. EHe>EN 2. EHe<EN 3. EHe=EN Two equally numbered moles of gas are confined to opposite sides of a sealed, insulated container. They are in thermal equilibrium with each other and the molecular mass of A is 4 times that of B. Which of the following statements are true regarding this situation? 1. The temperature of B is four times that of A. 2. The temperature of B is equal to the temperature of A. New Section 1 Page 2 3. 4. 5. 6. The average molecular speed of B is equal to that of A. The average molecular speed of B is twice that of A. The average kinetic energy of A is a fourth that of B. The total internal thermal energy of A is equal to B. One mole of an ideal gas initially has a set of state variables T 1, P1, V1. If the pressure is tripled while the temperature is held constant, what is the final volume in terms of the initial? 1. 2. 3. 4. 5. 9V1 3V1 V1 V1/3 V1/9 If the volume is doubled while the temperature is tripled, what is the final pressure in terms of the initial? 1. 2. 3. 4. 5. 6. 7. 8. P1/3 P1/2 2P1/3 P1 3P1/2 3P1/4 2P1 3P1 New Section 1 Page 3 Five points representing five different states of one mole of an ideal gas are labeled on the pressure–volume graph below. Rank the temperatures of the ideal gas in the labeled states. An ideal gas trapped in a cylinder expands while its pressure drops. The starting point for this process is labeled A and the endpoint is labeled B in the graph of pressure versus volume. This initial pressure, volume, and temperature are shown in the histograms. Complete the histograms, showing the final pressure, volume, and absolute temperature. New Section 1 Page 4 Two cylinders are filled to the same height H with ideal gases. The gases are different, and the cross sectional areas of the cylinders are different. Both cylinders have pistons that are free to move without friction. Is the temperature of the gas in cylinder A __________ the temperature of the gas in cylinder B? 1. greater than 2. less than 3. equal to Cylinders with equal cross-sectional areas contain different volumes of an ideal gas sealed in by pistons. There is a weight sitting on top of each piston. The gas is the same in all four cases and is at the same temperature. The pistons are free to move without friction. Rank the pressure of the gas in each cylinder. New Section 1 Page 5