MAE 241 – Homework 1 Page 1 of 3 MAE 241 – Spring 2019 – Homework 1 Administered 1/11/2019 – Due 11PM, Sunday 1/19/2019 to Gradescope Problem 1 – Review of units The Phoenix with a mass of 400 kg was a spacecraft used for exploration of Mars. Determine the weight of the Phoenix, in N, for the following situations: a. On the surface of Mars where the acceleration of gravity is 3.73 m/s2. b. On Earth where the acceleration of gravity is 9.81 m/s2. Problem 2 – review of chemistry A closed system consists of 0.4 kmol of octane (C8H18) occupying a volume of 2 m3. Determine: a. The weight of the system, in N. b. The molar-based specific volume, in m3/kmol. c. The mass-based specific volume, and m3/kg. Let g = 9.81 m/s2. Problem 3 – review of chemistry A closed vessel having a volume of 2.0 liter holds 2.0 x 1022 molecules of carbon dioxide gas. Determine: a. The number of moles, in kmol b. The mass of CO2 present, in kg and. c. The molar specific volume, in m3/kmol d. The specific volume of the CO2, in m3/kg. Hint: use Table A-1 of your textbook for molecular mass. Problem 4 – Quasistatic Equilibrium The figure below shows a gas contained in a vertical piston–cylinder assembly. A vertical shaft whose cross-sectional area is 0.8 cm2 is attached to the top of the piston. Determine the magnitude, F, of the force acting on the shaft, in N, required if the gas pressure is 300 kPa. The masses of the piston and attached shaft are 30 kg and 0.5 kg, respectively. The piston diameter is D = 10 cm. The local atmospheric pressure is 100 kPa. The piston moves smoothly and slowly at constant velocity in the cylinder and g = 9.81 m/s2. MAE 241 – Homework 1 Page 2 of 3 Problem 5– Measurement of Pressure a. For the tank shown in the figure below derive an expression to compute the Length, L, of the column of fluid as a function of density of the fluid in the manometer, 𝜌, and the atmospheric pressure, Patm. b. Determine the value of L when the manometer liquid is water and the tank contains a gas at a pressure of 1.5 bar. A barometer indicates the local atmospheric pressure is 750 mmHg. You also know that the density of water is 997 kg/m3 and the density of mercury is 13.59 g/cm3. Let g = 9.81 m/s2. Problem 6 – Gage pressure measurement A pressure gage mounted at the inlet to an air compressor indicates that the gage pressure is 60.0 kPa. The absolute pressure of the at the exit of the compressor is 5.5 times the absolute pressure at the inlet. The atmospheric pressure is 1.01 bar. What is the absolute pressure of the gas at the inlet and what is the gage pressure of the gas at the exit? Problem 7 – Unit conversions Perform the following unit conversions. Please do not use an on-line unit converter since this problem is given to you as practice in preparation for what you need to be proficient in: a. 170.8 in3 to L b. 1089.438 ft-lbf to kJ c. 140.0 hp to kW d. 1400.0 lb/h to kg/s e. 41.1488 lbf/in2 to kPa f. 3500.0 ft3/min to m3/s g. 105.0 mile/h to km/h h. 1.4 ton (=2000 lbf) to N Problem 8 – Newton’s second law Estimate the magnitude of the force, in lbf, exerted on a 20-lb goose in a collision of duration 1.5 x 10−3 s with an airplane taking off at 150 miles/h. Assume the bird’s velocity is zero before the collision. MAE 241 – Homework 1 Page 3 of 3 Problem 9 – Temperature conversions On January 3, 2019, in Flagstaff, AZ, the lowest temperature was 14oF at 5 AM and the highest 44oF at 4 PM. a. Express these temperatures in oR, K and oC. b. Determine the temperature change in oF, oR, oC and K from morning low to afternoon high. c. What is the relationship between the temperature changes in oF and oR? d. What is the relationship between the temperature changes in oC and K? Problem 10 – Ideal gas law application A closed deformable system consisting of 2 lb of air undergoes a process during which the relation between pressure and volume is defined by the mathematical expression PVn = Constant. The process begins with P1 = 20 lbf/in2, V1 = 15 ft3 and ends with P2 = 100 lbf/in2. The value of n = 1.3. Determine: a. The final volume, V2, in ft3 b. The specific volume at states 1 and 2, in ft3/lb. c. Use the ideal gas law as you learned in your chemistry course to determine the initial temperature, in °F. Hint: if you need the molecular mass of air please use Table A-1 or A-1E.

## MAE 241 – Homework 1 Page 1 of 3 MAE 241 – Spring 2019 – Homework 1 Administered 1/11/2019 – Due 11PM, Sunday 1/19/2019 to Gradescope Problem 1 – Review of units The Phoenix with a mass of 400 kg was a spacecraft used for exploration of Mars. Determine the weight of the Phoenix, in N, for the following situations: a. On the surface of Mars where the acceleration of gravity is 3.73 m/s2. b. On Earth where the acceleration of gravity is 9.81 m/s2. Problem 2 – review of chemistry A closed system consists of 0.4 kmol of octane (C8H18) occupying a volume of 2 m3. Determine: a. The weight of the system, in N. b. The molar-based specific volume, in m3/kmol. c. The mass-based specific volume, and m3/kg. Let g = 9.81 m/s2. Problem 3 – review of chemistry A closed vessel having a volume of 2.0 liter holds 2.0 x 1022 molecules of carbon dioxide gas. Determine: a. The number of moles, in kmol b. The mass of CO2 present, in kg and. c. The molar specific volume, in m3/kmol d. The specific volume of the CO2, in m3/kg. Hint: use Table A-1 of your textbook for molecular mass. Problem 4 – Quasistatic Equilibrium The figure below shows a gas contained in a vertical piston–cylinder assembly. A vertical shaft whose cross-sectional area is 0.8 cm2 is attached to the top of the piston. Determine the magnitude, F, of the force acting on the shaft, in N, required if the gas pressure is 300 kPa. The masses of the piston and attached shaft are 30 kg and 0.5 kg, respectively. The piston diameter is D = 10 cm. The local atmospheric pressure is 100 kPa. The piston moves smoothly and slowly at constant velocity in the cylinder and g = 9.81 m/s2. MAE 241 – Homework 1 Page 2 of 3 Problem 5– Measurement of Pressure a. For the tank shown in the figure below derive an expression to compute the Length, L, of the column of fluid as a function of density of the fluid in the manometer, 𝜌, and the atmospheric pressure, Patm. b. Determine the value of L when the manometer liquid is water and the tank contains a gas at a pressure of 1.5 bar. A barometer indicates the local atmospheric pressure is 750 mmHg. You also know that the density of water is 997 kg/m3 and the density of mercury is 13.59 g/cm3. Let g = 9.81 m/s2. Problem 6 – Gage pressure measurement A pressure gage mounted at the inlet to an air compressor indicates that the gage pressure is 60.0 kPa. The absolute pressure of the at the exit of the compressor is 5.5 times the absolute pressure at the inlet. The atmospheric pressure is 1.01 bar. What is the absolute pressure of the gas at the inlet and what is the gage pressure of the gas at the exit? Problem 7 – Unit conversions Perform the following unit conversions. Please do not use an on-line unit converter since this problem is given to you as practice in preparation for what you need to be proficient in: a. 170.8 in3 to L b. 1089.438 ft-lbf to kJ c. 140.0 hp to kW d. 1400.0 lb/h to kg/s e. 41.1488 lbf/in2 to kPa f. 3500.0 ft3/min to m3/s g. 105.0 mile/h to km/h h. 1.4 ton (=2000 lbf) to N Problem 8 – Newton’s second law Estimate the magnitude of the force, in lbf, exerted on a 20-lb goose in a collision of duration 1.5 x 10−3 s with an airplane taking off at 150 miles/h. Assume the bird’s velocity is zero before the collision. MAE 241 – Homework 1 Page 3 of 3 Problem 9 – Temperature conversions On January 3, 2019, in Flagstaff, AZ, the lowest temperature was 14oF at 5 AM and the highest 44oF at 4 PM. a. Express these temperatures in oR, K and oC. b. Determine the temperature change in oF, oR, oC and K from morning low to afternoon high. c. What is the relationship between the temperature changes in oF and oR? d. What is the relationship between the temperature changes in oC and K? Problem 10 – Ideal gas law application A closed deformable system consisting of 2 lb of air undergoes a process during which the relation between pressure and volume is defined by the mathematical expression PVn = Constant. The process begins with P1 = 20 lbf/in2, V1 = 15 ft3 and ends with P2 = 100 lbf/in2. The value of n = 1.3. Determine: a. The final volume, V2, in ft3 b. The specific volume at states 1 and 2, in ft3/lb. c. Use the ideal gas law as you learned in your chemistry course to determine the initial temperature, in °F. Hint: if you need the molecular mass of air please use Table A-1 or A-1E.

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Calculate the pOH of a solution at 25.0 °C that is 1.94 × 10-3 M in HCl. A) 1.00 B) 2.39 C) 2.72 D) 7.00 E) 11.3

## Calculate the pOH of a solution at 25.0 °C that is 1.94 × 10-3 M in HCl. A) 1.00 B) 2.39 C) 2.72 D) 7.00 E) 11.3

E) 11.3

If 2.891 g MgCl2 is dissolved in enough water to make 500.0 mL of solution, what is the molarity of the magnesium chloride solution? 5.782  10-3 M 1.518  10-2 M 0.5505 M 6.073  10-2 M 5.782 M 5.782  10-3 M 1.518  10-2 M 0.5505 M 6.073  10-2 M 5.782 M

## If 2.891 g MgCl2 is dissolved in enough water to make 500.0 mL of solution, what is the molarity of the magnesium chloride solution? 5.782  10-3 M 1.518  10-2 M 0.5505 M 6.073  10-2 M 5.782 M 5.782  10-3 M 1.518  10-2 M 0.5505 M 6.073  10-2 M 5.782 M

The solubility of Ar in water at 25°C is 1.6 × 10-3 M when the pressure of the Ar above the solution is 1.0 atm. The solubility of Ar at a pressure of 2.5 atm is __________ M. A) 1.6 × 103 B) 6.4 × 10-4 C) 4.0 × 10-3 D) 7.5 × 10-2 E) 1.6 × 10-3

## The solubility of Ar in water at 25°C is 1.6 × 10-3 M when the pressure of the Ar above the solution is 1.0 atm. The solubility of Ar at a pressure of 2.5 atm is __________ M. A) 1.6 × 103 B) 6.4 × 10-4 C) 4.0 × 10-3 D) 7.5 × 10-2 E) 1.6 × 10-3

Determine the changes in enthalpy , internal energy and entropy when 2.7 kg of water taken at P1 = 1.0133 X 10^5 Pa and T1 = 293 K evaporate at P2 = 0.50665 X 10^5 Pa and T2 = 373 K . Cp(l) ~ Cv(l) = 4.187 X 10^3 J/kg/K the specific heat of evaporation being 2260.98 X 10^3 J/kg

## Determine the changes in enthalpy , internal energy and entropy when 2.7 kg of water taken at P1 = 1.0133 X 10^5 Pa and T1 = 293 K evaporate at P2 = 0.50665 X 10^5 Pa and T2 = 373 K . Cp(l) ~ Cv(l) = 4.187 X 10^3 J/kg/K the specific heat of evaporation being 2260.98 X 10^3 J/kg

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