8. Compare the values obtained for the pressure(atm) of 2 mols O, at 298.15K held in a 8.25 dm bulb using a) Redlick-Kwong equation: For O;: Te = 154.6 K; Pc = 50.43 bar b) Beattie - Bridgeman equation For O2. the Beattie - Bridgeman constants: Ao = 0.14911 Pa m mol? Bo = 46.24 x 104m mol c= 4.80 x 10' m K mol a= 25.62 x 10*m mol b = 4.208 x 10 m mot Pa-m mole k Use R=8.314 VERST

1. The Helmholtz function of a certain gas is given by (V – F (T,V) = –nRT |1+ ln v – nb)T? an? пф V where n is the number of moles of gas, T is the temperatures of the gas, V is the volume of the gas, and a, b, and o are constants. (a) Derive the equation of state, the entropy, and the internal energy of the gas. (b) Suppose that 100 moles of the gas expands from 2 m3 to 5 m³ at 280 K and that the constants have the values a = 0.364 J m3 mol-2, b = 4.27 × 10-5 m³ mol-1, and $ = 1.09 × 10-5 m³ K³/2 mol-1. Calculate: (i) AU. (ii) the maximum energy that can be made available for work due to the process.

PHYSICAL CHEMISTRY:Calculate the pressure exerted by 1.0 mol C2H6 at 1000 K in 100 cm3 using (a) the ideal gas equation and (b) the van der Waals equation. The van der Waals constant for C2H6 are: a = 5.562 bar dm6 mol-2 ; b = 0.06380 dm3 mol-1 answer:[831; 1.72 x 10-3]

3. Potential density D is defined as the density of which dry air would attain if it were transformed reversibly and adiabatically from its existing conditions to a standard pressure po (usually 1000 mb). If the density and pressure of the air are p and p, respectively, it can be proven that the potential density can be expressed as, D = P(Pojev/cp P where cp and c, are the specific heats of air at constant pressure and constant volume, respectively. (a). Calculate the potential density of a quantity of air at a pressure of 600 mb and temperature -15 °C. (b) Show that 1 dD D dz == T (T₁-T) d where I'd is the dry adiabatic lapse rate, I the actual lapse rate of the atmosphere, and T the temperature at height z. [hint: cp - cv = R where R is the gas constant for dry air (R=287 Jdeg¹ kg-¹), cp=1004 Jdeg"¹ kg`¹, and cv=717 Jdeg`¹ kg-¹). (c) Show that the criteria for stable, neutral, and unstable conditions in the atmosphere are that the potential density decreases with height, is constant…