Under constant pressure P = 1 atm an ideal gas of 1.5 mol undergoes cooling from 120°C to 30.0°C, = 3/2R. Please calculate q, w, AU, and AH (all units are J). and Cv,m Please enter all four answers using scientific notation (E notation) with three significant figures, such as 2.30E4 (=23000). If the answer is negative, please do not forget the negative sign. If answer is zero, please just enter 0 without decimal. (1) q= (2) w= (3) AU= (4) ΔΗ=

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.

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…

Whenever a substance is heated, its enthalpy increases, as suggested by the relation, ∆?=Cp∆?. However, the molar heat capacity itself is a function of temperature, and for N2 this function can be modeled as                             ?p(?)=? + ?? + c / T2  where a= 28.58 J/mol·K, b= 0.00377 J/mol·K2, and c= –5.0 x 104J·K/mol. (a) What does this formula for heat capacity predict for the value of ?p(?)at 300K? (b) Now, compute the enthalpy change associated with heating 0.62 moles of N2 from 300 to 600 K using the formula for ?p (?), and report the answer in J. (c) What is the difference between this value and one computed using the constant value for Cp at 300 K from part (a)? Report the absolute value of the difference in J.