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- A PV diagram below, Figure 1, shows two possible states of a system containing three moles of a monatomic ideal gas. (P,= P2 = 450 Pa, V, = 2m', V,= 8m²) c. Draw the process which depicts an isothermal expansion from state 1 to the volume V, followed by an isochoric increase in temperature to state 2 and label this process (B). d. Find the change in internal energy of the gas for the two-step process (B) Figure 1 (N/m²) 500 ! 400+ 300+ 200+ 100 - + + + + 4 6. 8 10 V (m³) 2 Copyright © 2005 Pearson Prentice Hall, Inc.WA 4. a Th To Room temperature T = 293 K %3D V The gas volume changes from Vp to Va at constant temperature T. The cartoon on the right shows a piston of gas undergoing this compression while submerged in a container of room temperature water, which acts as a reservoir. The initial state of this process is a piston containing 2 moles of a monatomic gas at T, = 293 K (room temperature water) and volume V = 1.0 m. The gas is compressed until V, = 0.2 m. During the compression, the heat bath of room temperature water maintains the temperature of the gas at T = 293 K. Calculate the change in internal energy of the gas in joules during this process. Do not include units in your answer. Be careful to use the standard sign conventions for heat and work. Write your numerical answer in normal form as described above in the instructions to this worksheet. Click Save and Submit to save and submit. Click Save All Answers to save all answers. 28 F a7. Determine the missing properties and the phase descriptions in the following table for water. You may need help from the properties table. T, °C Р, КРа u, kJ/kg Phase X description A 175 0.6 В 110 1600 C 1500 2950 90 500 E 800 0.0
- (b) At initial state (state-1), a tank contains water vapor at 250°C with an unknown pressure. When the tank is cooled isochorically to 150°C at second state (state-2), the vapor starts condensing. Since the tank is not insulated, further heat loss occurred isobarically until all the water vapor in the tank turns to liquid at final state (state-3). (iv) Estimate the pressure, specific volume, and the enthalpy at its initial state; (v) Determine the pressure, specific volume, and enthalpy at state-3; and (vi) Sketch the process from initial to final state on a T-v diagram complete with the saturation line. Plot the point and pressure curve for each state, and show their axis values on the diagram. Describe the phases of each state in the calculations. Note: Show all steps and calculations involved.V. W. Th To %3D Room temperature T = 293 K V V. Vp The gas volume changes from Vp to Va at constant temperature T. The cartoon on the right shows a piston of gas undergoing this compression while submerged in a container of room temperature water, which acts as a reservoir. The initial state of this process is a piston containing 2 moles of a monatomic gas at Tc = 293 K (room temperature water) and volume V = a 1.0 m. The gas is compressed until V, = 0.2 m. During the compression, the heat bath of room temperature water maintains the temperature of the gas at T 293 K. Calculate the work done in joules by the gas during this process. Do not include units in your answer. Be careful to use the standard sign convention for work done by the gas. Write your numerical answer in normal form as described above in the instructions to this worksheet.2. Consider a metal rod with the equation of state L- Lo = Lo +a(T YA %3D Here Lo, Y, A, To, and a are constants,T is the temperature, L is the length, and F is the tension. Work is given by dW a) Using the first law and the expression for dU in terms of it partial derivatives with respect to T and L, show that for this system -FdL. (). -). G). (4). - se, b) By differentiating the first of these equations with respect to L and the second with respect to T show that ), -r(器). =F-T ƏT c) Using the above result and the equation of state, find an expression for (0/aL). Then, assuming that C. the heat capacity at constant length is a Constant. find an expression for the internal energy, U, as a function of T and L.
- 3-21 Complete this table for H,O: T, °C Р, КРа u, kJ/kg Phase description 400 1450 220 Saturated vapor 190 2500 4000 3040 3-22 Complete this table for H,O: T, °C Р. КРа U, m'/kg Phase description 140 0.035 550 Saturated liquid 125 750 300 0.140● Determine the missing properties and the phase descriptions in the following table for water: T, °C 125 75 P, KPa 200 1000 500 800 u, kJ/kg 1600 2950 X 0.6 0.0 Phase Description2. Given a closed container of volume 1 L containing 50 g of helium gas, calculate the following: a. The pressure at T = 6 K, assuming that the gas is an ideal gas. b. The pressure at T of state. = 6 K, assuming that the gas obeys van der Waal's equation c. The pressure at T 6 K, assuming that the gas obeys the virial equation of state truncated after the second term. = d. The state of the fluid at T = 4.2 K. (Hint: 4.2 K is below T. and 50 kg/m³ is greater than p, @ 4.2 K.)
- 3. Find the coefficient of thermal expansion a and the isothermal compressibility k from each of the following p-v-T relations: RT (a) Ideal gas equation, p = (b) Dieterici equation, p = RT e-a/RTU RT aRTV In 2b (c) Saha-Bose equation, p = In the above equations R is the gas constant and a and b are specific constants. Verify that for large values of T and v all the expressions for and K go over into the corresponding expressions for an ideal gas.Complete this table for refrigerant-134a: Р, КРа 600 h, kJ/kg 180 T, °C Phase Description -10 0.6 -14 500 1200 300.63 44 1.0Question 2 (a) Determine the missing properties and the phase descriptions in the following table for water: T,°C Р, КРа v,m³ /kg Phase description i. 200 1400 ii. 500 0.20