THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I
THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I
8th Edition
ISBN: 9781307434316
Author: CENGEL
Publisher: INTER MCG
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Chapter 3.8, Problem 97P

Nitrogen at 150 K has a specific volume of 0.041884 m3/kg. Determine the pressure of the nitrogen using (a) the ideal-gas equation and (b) the Beattie-Bridgeman equation. Compare your results to the experimental value of 1000 kPa.

(a)

Expert Solution
Check Mark
To determine

The pressure of the nitrogen using the ideal gas equation.

Answer to Problem 97P

The pressure of the nitrogen using the ideal gas equation is 1063kPa_.

Explanation of Solution

Determine the pressure of the tank using the ideal gas equation.

P=RTv (I)

Here, the universal gas constant is R, the specific volume of the tank is v, and the temperature of the tank is T.

Conclusion:

Refer to Table A-1 to find the gas constant and molar mass of nitrogen as 0.2968kPam3/kgK and 28.013kg/kmol.

Substitue 0.2968kPam3/kgK for R, 150K for T, and 0.041884m3/kg for v in Equation (I).

P=(0.2968kPam3/kgK)(150K)(0.041884m3/kg)=(44.52kPam3/kg)(0.041884m3/kg)=1062.9kPa1063kPa

Therefore, the error compression with the actual value is 6.3%.

Thus, the pressure of the nitrogen using the ideal gas equation is 1063kPa_.

(b)

Expert Solution
Check Mark
To determine

The pressure of the nitrogen using the Beattie-Bridgeman equation.

Answer to Problem 97P

The pressure of the nitrogen using the Beattie-Bridgeman equation is 1000.4kPa_.

Explanation of Solution

Determine the pressure in the tank using the Beattie-Bridgeman equation.

P=RuTv¯2(1cv¯T3)(v¯+(B0(1bv¯)))(A0(1av¯))v¯2=RuT(Mv)2(1c(Mv)T3)((Mv)+(B0(1b(Mv))))(A0(1a(Mv)))(Mv)2 (II)

Here, the five constant are A0,a,B0,b,andc.

Conclusion:

From the Table 3-4, “Constant that appear in the Beattie-Bridgeman and the Benedict-Webb-Rubin equation of state” to obtain of value of the five constant are A0,a,B0,b,andc as 136.2315, 0.02617, 0.05046, -0.00691, and 4.20×104.

Substitute 136.2315 for A0, 0.02617 for a, 0.05046 for B0, -0.00691 for b, 4.20×104m3K3/kmol for c, 0.041884m3/kg for v, 28.013kg/kmol for M 150K for T, and 8.314kPam3/kmolK for R in Eqaution (IV).

P=[((8.314kPam3/kmolK)(150K)((28.013kg/kmol)×(0.041884m3/kg))2)×(1(4.20×104m3K3/kmol)((28.013kg/kmol)×(0.041884m3/kg))(150K)3)×(((28.013kg/kmol)×(0.041884m3/kg))+((0.05046)(1(0.00691)((28.013kg/kmol)×(0.041884m3/kg)))))((136.2315)(1(0.02617)((28.013kg/kmol)×(0.041884m3/kg))))((28.013kg/kmol)×(0.041884m3/kg))2]=[((1247.1kPam3/kmol)(1.1733m3/kmol)2)×(1(4.20×104m3K3/kmol)(1.1733m3/kmol)(3375000K3))×((1.1733m3/kmol)+(0.05076m3/kmol))(133.193m3/kmol)(1.1733m3/kmol)2]=[((1247.1kPam3/kmol)(1.615203m6/kmol2))×(1(4.20×104m3K3/kmol)(1.1733m3/kmol)(3375000K3))×((1.1733m3/kmol)+(0.05076m3/kmol))(133.193m3/kmol)(1.615203m6/kmol2)]=1000.4kPa

Therefore, the error compression with the actual value is negligible error.

Thus, the pressure of the nitrogen using the Beattie-Bridgeman equation is 1000.4kPa_.

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Chapter 3 Solutions

THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I

Ch. 3.8 - Does the amount of heat absorbed as 1 kg of...Ch. 3.8 - Does the reference point selected for the...Ch. 3.8 - What is the physical significance of hfg? Can it...Ch. 3.8 - Does hfg change with pressure? How?Ch. 3.8 - Is it true that it takes more energy to vaporize 1...Ch. 3.8 - What is quality? Does it have any meaning in the...Ch. 3.8 - Which process requires more energy: completely...Ch. 3.8 - In the absence of compressed liquid tables, how is...Ch. 3.8 - Prob. 19PCh. 3.8 - Complete this table for H2O:Ch. 3.8 - Prob. 21PCh. 3.8 - Complete this table for H2O:Ch. 3.8 - Complete this table for H2O:Ch. 3.8 - Prob. 26PCh. 3.8 - Complete this table for refrigerant-134a:Ch. 3.8 - A 1.8-m3 rigid tank contains steam at 220C....Ch. 3.8 - A pistoncylinder device contains 0.85 kg of...Ch. 3.8 - Prob. 30PCh. 3.8 - 3–31 10-kg of R-134a fill a 1.348-m3 rigid...Ch. 3.8 - Prob. 32PCh. 3.8 - Refrigerant-134a at 200 kPa and 25C flows through...Ch. 3.8 - Prob. 34PCh. 3.8 - The temperature in a pressure cooker during...Ch. 3.8 - Prob. 36PCh. 3.8 - 3–37E One pound-mass of water fills a 2.4264-ft3...Ch. 3.8 - Prob. 38PCh. 3.8 - Water is to be boiled at sea level in a...Ch. 3.8 - Repeat Prob. 340 for a location at an elevation of...Ch. 3.8 - 10 kg of R-134a at 300 kPa fills a rigid container...Ch. 3.8 - 100 kg of R-134a at 200 kPa are contained in a...Ch. 3.8 - Water initially at 200 kPa and 300C is contained...Ch. 3.8 - 3–44 Saturated steam coming off the turbine of a...Ch. 3.8 - Prob. 45PCh. 3.8 - Prob. 46PCh. 3.8 - Water is being heated in a vertical pistoncylinder...Ch. 3.8 - Prob. 49PCh. 3.8 - A rigid tank with a volume of 1.8 m3 contains 40...Ch. 3.8 - A pistoncylinder device contains 0.005 m3 of...Ch. 3.8 - 3–53E A 5-ft3 rigid tank contains 5 lbm of water...Ch. 3.8 - A 5-ft3 rigid tank contains a saturated mixture of...Ch. 3.8 - Superheated water vapor at 180 psia and 500F is...Ch. 3.8 - Prob. 57PCh. 3.8 - 3–58 A rigid tank contains water vapor at 250°C...Ch. 3.8 - A pistoncylinder device initially contains 1.4 kg...Ch. 3.8 - How much error would one expect in determining the...Ch. 3.8 - Prob. 61PCh. 3.8 - 3–62 A rigid vessel contains 8 kg of...Ch. 3.8 - A rigid tank initially contains 1.4 kg saturated...Ch. 3.8 - A pistoncylinder device initially contains 50 L of...Ch. 3.8 - Under what conditions is the ideal-gas assumption...Ch. 3.8 - Prob. 66PCh. 3.8 - Propane and methane are commonly used for heating...Ch. 3.8 - A 400-L rigid tank contains 5 kg of air at 25C....Ch. 3.8 - Prob. 69PCh. 3.8 - Prob. 70PCh. 3.8 - The pressure gage on a 2.5-m3 oxygen tank reads...Ch. 3.8 - A spherical balloon with a diameter of 9 m is...Ch. 3.8 - Reconsider Prob. 373. Using appropriate software,...Ch. 3.8 - Prob. 74PCh. 3.8 - Prob. 75PCh. 3.8 - A rigid tank whose volume is unknown is divided...Ch. 3.8 - Prob. 77PCh. 3.8 - Prob. 78PCh. 3.8 - Prob. 79PCh. 3.8 - Prob. 80PCh. 3.8 - Prob. 81PCh. 3.8 - Determine the specific volume of superheated water...Ch. 3.8 - Determine the specific volume of superheated water...Ch. 3.8 - Prob. 85PCh. 3.8 - Prob. 86PCh. 3.8 - Prob. 87PCh. 3.8 - Prob. 88PCh. 3.8 - Prob. 89PCh. 3.8 - Prob. 90PCh. 3.8 - Carbon dioxide gas enters a pipe at 3 MPa and 500...Ch. 3.8 - A 0.016773-m3 tank contains 1 kg of...Ch. 3.8 - What is the physical significance of the two...Ch. 3.8 - A 3.27-m3 tank contains 100 kg of nitrogen at 175...Ch. 3.8 - Prob. 95PCh. 3.8 - Refrigerant-134a at 400 psia has a specific volume...Ch. 3.8 - Nitrogen at 150 K has a specific volume of...Ch. 3.8 - A 1-m3 tank contains 2.841 kg of steam at 0.6 MPa....Ch. 3.8 - Prob. 102PCh. 3.8 - Prob. 103PCh. 3.8 - On a certain day, the temperature and relative...Ch. 3.8 - Prob. 105PCh. 3.8 - Consider two rooms that are identical except that...Ch. 3.8 - A thermos bottle is half-filled with water and is...Ch. 3.8 - Prob. 108RPCh. 3.8 - The combustion in a gasoline engine may be...Ch. 3.8 - A tank contains argon at 600C and 200 kPa gage....Ch. 3.8 - Prob. 111RPCh. 3.8 - Prob. 112RPCh. 3.8 - A rigid tank with a volume of 0.117 m3 contains 1...Ch. 3.8 - Prob. 114RPCh. 3.8 - Ethane at 10 MPa and 100C is heated at constant...Ch. 3.8 - Prob. 116RPCh. 3.8 - A 10-kg mass of superheated refrigerant-134a at...Ch. 3.8 - A 4-L rigid tank contains 2 kg of saturated...Ch. 3.8 - The gage pressure of an automobile tire is...Ch. 3.8 - Prob. 120RPCh. 3.8 - Steam at 400C has a specific volume of 0.02 m3/kg....Ch. 3.8 - A tank whose volume is unknown is divided into two...Ch. 3.8 - Prob. 123RPCh. 3.8 - Prob. 124RPCh. 3.8 - Prob. 125RPCh. 3.8 - A tank contains helium at 37C and 140 kPa gage....Ch. 3.8 - Prob. 127RPCh. 3.8 - Prob. 131RPCh. 3.8 - Consider an 18-m-diameter hot-air balloon that,...Ch. 3.8 - Prob. 134FEPCh. 3.8 - Water is boiled at 1 atm pressure in a coffeemaker...Ch. 3.8 - Prob. 136FEPCh. 3.8 - Prob. 137FEPCh. 3.8 - Water is boiled in a pan on a stove at sea level....Ch. 3.8 - Prob. 139FEPCh. 3.8 - Consider a sealed can that is filled with...Ch. 3.8 - A rigid tank contains 2 kg of an ideal gas at 4...Ch. 3.8 - The pressure of an automobile tire is measured to...
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