Answered step by step
Verified Expert Solution
Question
1 Approved Answer
need help with these two questions. Thanks As shown in the figure, a cylinder with a moveable piston and containing a monatomic ideal gas in
need help with these two questions. Thanks
As shown in the figure, a cylinder with a moveable piston and containing a monatomic ideal gas in an initial state A undergoes an isovolumetric, then an isothermal, and finally an isobaric process to complete the cycle. I' (aim) I! \\'(l.) (B When the gas is in the initial state, the volume is 3.00 L, the pressure is 1.00 atm, and the temperature is 300 K. The gas is rst warmed at constant volume to a pressure of 2 times the initial value (state B). The gas is then allowed to expand isothermally to some new volume (state C). Finally it is compressed isobarically to its initial state. (Due to the nature of this problem, do not use rounded intermediate values in your calculationsincluding answers submitted in WebAssign.) (a) Find the number of moles of the gas. -x Since we have an ideal gas, knowing the pressure, temperature, and volume of the gas at one time, we can use the ideal gas law to determine the number of moles of the gas. Don't forget to 3 convert the units for pressure from atm to N/m2 and the units for volume from L to m . moles (b) Find the temperature of the gas at state B (in K). -x Write the ideal gas law for states A and B and then combine them in such a manner that you eliminate the volume (which is constant for the process) and any other constants in order to obtain a relationship between the temperature and pressure of the gas in states A and B. K (c) Find the temperature of the gas at state C (in K). -x Write the ideal gas law for states A and B and then combine them in such a manner that you eliminate the volume (which is constant for the process) and any other constants in order to obtain a relationship between the temperature and pressure of the gas in states A and B. K (d) Find the volume of the gas at state C (in L). -L (e) Determine values (in kJ) for Q, W, and AE - l_l int for the process A > B. (e) Determine values (In kJ) for Q, W, and Mint tor the process A > B. Q int W X What can you say about the work done on the gas for an isovolumetric process? How does the change in internal energy depend on the change in temperature? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. k] W wk] X What can you say about the work done on the gas for an isovolumetric process? How does the change in internal energy depend on the change in temperature? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred k] (f) Determine values (in kJ) for Q, W, and AEint for the process B > C. Q AE. int ll 0 0 0 (9) Determine values (in Q int I] X What can you say about the change in internal energy for an isothermal process? How can you determine the work done on the gas for an isothermal process? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. kJ X What can you say about the change in internal energy for an isothermal process? How can you determine the work done on the gas for an isothermal process? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred kJ ykJ kJ) for Q, W, and A5 for the process C > A. int 0 energy and 0 energy and 0 X How does the change in internal energy depend on the change in temperature? How can you determine the work done on the gas for an isobaric process? Knowing the change in internal the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. kJ X How does the change in internal energy depend on the change in temperature? How can you determine the work done on the gas for an isobaric process? Knowing the change in internal the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. k] X How does the change in internal energy depend on the change in temperature? Howe can you determine the work done on the gas for an isobaric process? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. k] (h) Determine values (in kJ) for Q, W, and AEint for the complete cycle A > B > C > A. Q E X If the gas undergoes a complete cycle, and initial and nal states are identical, what can we say about the change in internal energy for the cycle? Knowing the work done on the gas and the hea E t transfer for each process of the cycle, how can we determine these quantities for the complete cycle? How can you use the rst law of thermodynamics to check your work? X If the nas Iinrlernnec a rnmnlete rvrle, and initial and nal etater. are identical, what can we saw ahmit the rhanne in internal enernv for the rvrle? Knnwinn the work done nn the na: A triatomic molecule can have a linear configuration, as does C02 (Figure a), or it can be nonlinear, like H20 (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. 0 (3 0 ya} J El 0 3/ \\ '3 o (a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear? EintT = 2 x (b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear? EintT = X At high temperatures, a triatomic molecule has two modes of vibration, and each contributes %R to the molar specific heat for its kinetic energy and another %R for its potential energy. (c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary: R.) EintT = 4R X (d) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the nonlinear molecules. (Use the following as necessary: R.) EintT = 6R X Are the data in table below sufficient to make this determination? O Yes O No Figure Monatomic Gases Diatomic Gases Polyatomic Gases Molar Specific Heats of Various Gases Molar Specific Heat (J/mol . K) Gas Cp Cy Cp - Cy y = Cp/ Cy Monatomic gases He 20.8 12.5 8.38 1.67 Ar 20.8 12.5 8.38 1.67 Ne 20.8 12.7 8.12 1.64 Kr 20.8 12.3 8.49 1.69 Diatomic gases H2 28.8 20.4 8.38 1.41 29.1 20.8 8.38 1.40 O2 29.4 21.1 8.38 1.40 CO 29.3 21.0 8.38 1.40 Cl, 34.7 25.7 8.96 1.85 Polyatomic gases CO2 37.0 28.5 8.50 1.80 SO, 40.4 31.4 9.00 1.29 H,O 85.4 27.0 8.37 1.30 CHA 35.5 27.1 8.41 1.81 * All values except that for water were obtained at 800 K.Figure Monatomic Gases Diatomic Gases Polyatomic Gases Gas Cp CV Cp - Cv Y = Cp / Cv He 20.8 12.5 8.33 1.67 Ar 20.8 12.5 8.33 1.67 Ne 20.8 12.7 8.12 1.64 Kr 20.8 12.3 8.49 1.69Figure Monatomic Gases Diatomic Gases Polyatomic Gases Gas Cp Cv Cp - Cv| Y = Cp / Cv CO2 37.0 28.5 8.50 1.30 SO , 40.4 31.4 9.00 1.29 H,O 35.4 27.0 8.37 1.30 CH 4 35.5 27.1 8.41 1.31Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started