3.(10%) If volumetric equation of state can be expanded in the form of Virial equation of state, show that Boyle temperature (T_B) for the volumetric equation of state is written in terms of a, b, and R.

1. (15%) The pressure derivative of entropy at the constant temperature is written in termns ofP. Ifliquid ammonia at 350 K is compressed from saturation pressure of 270 kPa to 1000 kPa, determine its enthalpy (△H, kJ/kg) and entropy (△S, kJ/kg-K) changes. For saturated liquid ammonia at 350 K, liquid volume and volume cxpansivity (β) are 1.551 x 10-3 m3• kg-1and2.095 x 10-3 K-1, respectively.

2. (15%) Air (molar mass - 28.851 g/mol) enters a compressor through a 5-cm-radius tube with an average velocity of 10 m•s-1 at the initial conditions [P1 = 1 bar and T1 = 10℃], and is discharged through a 1.5-cm-radius tube at the final conditions [P2 = 36 bar and T2 = 90℃]. The shaft work supplied to the compressor is 25.0 kJ-mol-1. Determine the heat-transfer rate (kJ/sec) from the compressor? Assume enthalpy and specific volume at initial condition are 30.68 kJ mol-1and 31.40 L ' mol-1, respectively, while enthalpy and specific volume at final condition are 33.97 kJ ㆍ mol-1 and 0.5438 L ㆍ mol-1, respectively. 

4. (10%) A refrigeration system cools a steel casting from 25℃ to -15℃ at a rate of 15 kg．s-1 Assume that heat flows from the refrigeration system to the surroundings at a temperature of 45℃ and the specific heat capacity of the steel casting is 7.6 kJ．kg-1.℃-1. If the thermodynamic efficiency of the process is 31%, determine the power (kJ/kg) requirement of the system? 

5. (12%) A liquid-phase reaction A →2R was performed in a CSTR with a volume of 5 L. In the reaction, the reactant A was fed to the CSTR at a concentration of I molL. The researcher intended to find a rate expression for this reaction by carrying out the experiments at different conditions, which were summarized in the following Table. Please determine the reaction order and the activation energy of this reaction.

(a) Is it likely that film resistance to mass transfer infuence the rate? (5%)

(b) Could this run have been made in the regime of strong pore diffusion? (5%)

(c) Would you expect to have temperature variations within the pellet or across the gas film?(5%) 

7. (11%) In an ammonia decomposition reaction to generate N2 and H2 on a Platinum catalyst (2NH3 → N2 + 3H2) the rate can be expressed as -r = kKAPA/KHPH, where k is the rate constant, PA and PH indicate the pressures of ammonia and hydrogen, and KA and KH are the adsorption constants for ammonia and hydrogen. Suggest a mechanism and the assumptions consistent with the rate equation and prove it.

(A) The reaction is exothermic: (1) Ture, (2) False), (3) Cannot tell (3%)

(B) The reaction is endothermic: (1) Ture, (2) False), (3) Cannot tell (3%)

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