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• tanisha gupta

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Autumn 2019-20

MIN 106: ENGINEERING THERMODYNAMICS Tutorial Sheet 3 Properties of Pure Substances –II I

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Explain: i Compressibility Factor ii Principle of corresponding State iii Generalized Compressibility Chart. A tank contains 0.05 m3 of N2 at -21O C and 10MPa. Determine mass of Nitrogen in kg i using the ideal gas model ii data from the compressibility chart Comment on the applicability of the ideal gas model for nitrogen at this state. (6.685 kg, 6.973 kg) For what ranges of pressure and temperature can air be considered an ideal gas? Explain your reasoning. Determine the temperature, in K, of oxygen (O2) at 250 bar and a specific volume of 0.003 m3/kg using generalized compressibility data and compare with the value obtained using the ideal gas model. (308 K, 288.66K) The pressure within a 23.3 m3 tank should not exceed 105 bar. Check the pressure within the tank if filled with 1000 kg of water vapor maintained at 360 O C using the (i) ideal gas equation of state. (ii) van-der Waals equation of state. (iii) Redlich-Kwong Equation (iv) compressibility chart (v) steam tables. (125.34, 103.76, 101.34, 101.496, 100) A rigid tank contains 1 kg of O2 at P1 40 bar, T1 180 K. The gas is cooled until the temperature drops to 150 K. Determine the volume in the tank, in m 3, and final pressure, in bar, using (i) the ideal gas equation of state. (ii) Redlich-Kwong Equation state (iii) compressibility chart (0.0117 m3, 33.33 bars; 9.418x10-3m3, 30.204 bars; 9.66x10-3 m3, 30.3 bars) A tank with volume 10 m3 is used to store propane at 35 bars and 100O C. Calculate the mass of gas, in kg, using (a) ideal gas model (b) compressibility chart. If gas is withdrawn from the tank in an isothermal process, find from the compressibility chart, the pressure at which half of the original mass as per (b) remains in the tank. (497.4 kg, 814.1 kg, 22.2 bars) Calculate the specific volume, in m3/kmol of Nitrogen at 102 bars and -450 C by (i) ideal gas equation (ii) the virial equation Pv = a +bP + cP2 + dP3. The virial coefficients for Nitrogen at this temperature are: b = -2.34x10-2, c = 3.61x10-5 and d = 5.18x10-7 where P is in bars, T is in Kelvin and v is in m3/kmol. (0.1858 m3/kmol, 0.1715 m3/kmol) 𝜕𝑃

𝜕

𝜕𝑃

Using the fact that (𝜕𝑣 ) and(𝜕𝑣 (𝜕𝑣 )) must be zero at the critical point, find the 𝑇

𝑇

constants a and b for the van-der Waal’s equation, in terms of Pc and Tc. Also, find the value of compressibility factor at the critical point. 𝟐𝟕 𝟏 𝑹𝑻 (𝒂 = 𝟔𝟒 𝑹𝟐 𝑻𝟐𝒄 𝑷 , 𝒃 = 𝟖𝑷𝒄 , 3/8) 𝒄

𝒄

Following data may be used

SUBSTANCE

MOLECULAR WEIGHT 28.97 28.01 32 44.09 18.02

AIR NITROGEN OXYGEN PROPANE WATER

CRITICAL TEMPERATURE, K 133 126 154 370 647.3

Constants for van-der Waals and Redlich – Kwong equations Water van-der Waals constants 𝑚3

2

a = 5.531 𝑏𝑎𝑟 (𝑘𝑚𝑜𝑙)

b =0.0305

𝑚3 𝑘𝑚𝑜𝑙

Redlich – Kwong Constants 𝑚3

2

𝑚3

2

𝑚3

2

a = 142.59 𝑏𝑎𝑟 (𝑘𝑚𝑜𝑙) 𝐾 1/2 b = 0.02111 𝑏𝑎𝑟 (𝑘𝑚𝑜𝑙 ) Oxygen Redlich – Kwong Constants 𝑚3

2

a = 17.22 𝑏𝑎𝑟 (𝑘𝑚𝑜𝑙) 𝐾 1/2 ; b = 0.02197 𝑏𝑎𝑟 (𝑘𝑚𝑜𝑙)

CRITICAL PRESSURE, BARS 37.7 33.9 50.5 42.7 220.9