Ch 2 Online HW

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Physics 132 Online Homework Problem: Chapter 2 Problem 1. (Nitrogen as an Ideal Gas) A. How many moles of nitrogen are there in 7 kg of nitrogen? The molecular weight of nitrogen is 28 g/mol . B. What is the pressure (in Pa ) of 7 kg of nitrogen gas confined to a volume of 0 . 4 m ! at 20 °C ? Problem 2. (The Ideal Gas Law) An ideal gas in container 1 has pressure � , volume � , temperature � , and in container 2 with pressure 2 � , volume " # and temperature 2 � . What is the ratio of the number of moles of this gas in the two containers, $ ! $ " ? Problem 3. (Properties of an Ideal Gas) A sample of ideal gas is in a sealed container. The temperature of the gas and the volume of the container are both increased. What other properties of the gas necessarily change? More than one answer may be correct. a. The average (or rms, root-mean-square) speed of the gas atoms. b. The thermal energy of the gas. c. The pressure of the gas.

d. The number of molecules of gas Problem 4. (Volume of an Ideal Gas) What volume, in liters , is occupied by 1 �� of an ideal gas at a pressure of 1 atm and a temperature of 0 °C ? ( 1 = 1.01 × 10 �� % Pa ). Express your answer in liters to the tenth decimal place. Problem 5. (An Ideal Gas Process) A. What is the ratio � & � ' ? for the process shown in the right? B. How much work is done in this process? Express your answer in joules . Problem 6. (Internal Energy, Work done, Heat flow in an Ideal Gas Process) A cylinder with a moveable piston contains 0.016 mol of helium. A researcher expands the gas via a process show in the figure below. A. Using the ideal gas law, what is the initial temperature of the system? Express you answer in Kelvin .

B. What is the final temperature of the system? Again, express your answer in Kelvin. C. What is the change in internal energy for the process? Remember the relation: Express your answer in joules . Δ � '() = � 3 2 � * Δ � D. How much work is done by the gas during this process? This can be done by finding the area underneath the curve by splitting it into a rectangle and a triangle. Again, express your answer in joules . E. Putting it all together, how much heat needs to be transferred into or out of the system? Use positive for heat added to the system and negative for removed heat. Express you answer in joules . Problem 7. (The First Law of Thermodynamics)

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500 J of work is done on a gas in a process that decreases the system’s thermal energy by 300 J . A. During this process: a. Heat is absorbed by the system b. Heat is released by the system c. No heat is exchanged B. How much energy (in J ) is transferred to the system as heat? Write your answer in joules. (Hint: Check the text to see how the signs of � , � , and Δ � are defined.) C. Is the gas expanding or contracting? a. Expanding b. Contracting D. Which of the following ideal-gas processes could this process be? Choose all that apply. a. Isobaric b. Isochoric c. Isothermal d. Adiabatic Problem 8. (Work done on a gas) A gas in a cylinder with a movable piston occupies 50.0 cm ! at 50 °C . The gas is cooled at constant pressure until the temperature reaches 10 °C . A. What is the final volume? Express your answer in units of cubic centimeters. B. This change happens at a pressure of 1.5 atm . How much work is done on the gas? Express your answer in joules .

Problem 9. (Change in Enthalpy) A system containing 10 mol of an ideal gas is maintained at thermal equilibrium (at the same temperature) as its surroundings, at a temperature of 50 °C . It then has 100 kJ of heat transferred to it, which causes it to expand isothermally against a constant pressure of 1 atm . It is then isothermally compressed back to its initial volume. What is its change in enthalpy over the entire process? Express your answer in units of kJ . Problem 10. (Ideal Gas Processes) A. Isochoric, or isovolumetric, processes are ones where the volume remains constant. During the isochoric process represented by the graph, which of the following is true? a. No heat is exchanged with the system. b. No work is done on the system. c. The change in internal energy is negative. d. The change in temperature is zero. B. An isobaric process is one where the pressure remains constant. Using the figure, evaluate if the following statement is true or false: the environment does positive work on the gas. a. True b. False C. During an isothermal process, the temperature remains constant. Which of the following statements about the isotherm in the figure is true? Hint: remember the first law of thermodynamics.

a. The change in internal energy is positive. b. The work done on the system is all expelled as heat energy. c. The change in internal energy is negative. d. The system does no work. D. An adiabatic process is one where there is no heat exchange between the system and the environment. While the curve of the graph looks like the isothermal process, the work done on the system changes the temperature—two isotherm lines are included to contrast with the bolded adiabatic line. During the adiabatic compression shown in the figure, which of the following is true? a. The change in internal energy is negative. b. The work done on the system is zero. c. The work done on the system is equal to the change in internal energy. d. The final temperature is lower than the initial temperature. Problem 11. (Cyclic Process) Two moles of an ideal gas is taken through the cyclic process → → → → � � � � � as shown. A. Calculate the work done on the gas during process AB. Express your answer in units of kJ .

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B. Calculate the work done on the gas during process BC. Express your answer in units of kJ . C. Calculate the work done on the gas during process CD. Express your answer in units of kJ . D. Calculate the work done on the gas during process DA. Express your answer in units of kJ . E. Use your answers to the previous parts of work done on the gas to calculate the total work done by the gas during the process ABCD, and express your answer in kJ . (Note: you can verify your answer by calculating the total area inside the curve on the PV diagram.) Problem 12. (Change in Enthalpy from Change in Internal Energy) The temperature of 5 mol of hydrogen in a sealed chamber at 1 atm decreases by 50 K . If the corresponding change in internal energy is 255 J , what is the change in enthalpy? Express your answer in units of joules .

Problem 13. (Exothermic versus Endothermic Processes) A. Which of the following graphs belongs to an exothermic process? a b B. Which of the following statements about the change in enthalpy are true of an exothermic process? Choose all that apply. a. ∆ < 0 � b. ∆ > 0 � c. ∆ = 0 � Problem 14. (Partial Pressure) A. A container holds a mixture of oxygen and nitrogen at a total pressure of 2 atm . If there are 1 mol of oxygen and 3 mol of nitrogen here, what is the partial pressure of oxygen? Express your answer in units of atm . B. If the oxygen were replaced with the same molar concentration of hydrogen gas (with a much smaller atomic mass), which of the following would be true? Assume the temperature remains the same. a. The total pressure would increase. b. The partial pressure of the hydrogen would be less than that of the oxygen it replaced. c. The partial pressure of the nitrogen would increase. d. The partial pressure of the hydrogen would be exactly the same as that of the oxygen it replaced.

Problem 15. (Partial Pressure in Alveoli) A. Alveoli are the tiny air sacs that make up the lungs. The total pressure of the alveoli is about 760 mmHg . If the composition of the alveolar gases is 13.7% oxygen, 5.2% CO 2 , 74.9% N 2 , and 6.2% H 2 O i. Calculate the partial pressure of O 2 . Express your answer in units of mmHg. ii. Calculate the partial pressure of CO 2 . Express your answer in units of mmHg. B. The partial pressures of oxygen and carbon dioxide in the blood are � +, = 40 mmHg and � -+, = 47 mmHg . Use this with your calculated answers in part A to determine which of the following statements are correct. Remember that the diffusion happens along the pressure gradient, from a region of higher pressure to a region of lower pressure a. Oxygen diffuses down its pressure gradient, moving out of the alveoli and entering the blood in the capillaries. b. Oxygen diffuses down its pressure gradient, moving out of the blood in the capillaries and into the alveoli. c. Carbon di-oxide diffuses down its pressure gradient, moving out of the capillaries and into the alveoli. d. Carbon di-oxide diffuses down its pressure gradient, moving out of the alveoli and into the blood in the capillaries.

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