Question

3.9-4. Compute Cp, Cu, Ks, and Ky for the system in Problem 1.10-1(a). With these values corroborate the validity of equations 3.75 and 3.76. R21/3 a) S = 3) (NVUJI 0.0 The coefficient of thermal expansion is defined by 1/ av var (6) - FCT). (3.67) The coefficient of thermal expansion is the fractional increase in the volume per unit increase in the temperature of a system maintained at constant pressure (and constant mole numbers). The isothermal compressibility is defined by кт 1/ au vlap H).- Home 1/av И\ ӘР (3.68) T The isothermal compressibility is the fractional decrease in volume per unit increase in pressure at constant temperature. The molar heat capacity at constant pressure is defined by 1 :), P )--) as T as dg (3.69) 07 NdTP The adiabatic compressibility is defined by 1/ Ou 1/ V (3.73) ulap vlap This quantity characterizes the fractional decrease in volume associated with an isentropic increase in pressure (i.e., for a system that is adiabati- cally insulated). The molar heat capacity at constant volume, defined by as Tas 1/dQ =T (3.74) әТ NdTv measures the quasi-static heat flux per mole required to produce unit increase in the temperature of a system maintained at constant volume. Cp = + TVa? NKI (3.75) and TVa? Kg = kgt (3.76) Ne,

Also known are the Equations of State in the Entropy form:

$\frac{1}{T}=\left (\frac{\partial S}{\partial U} \right )_{V,N} and \frac{P}{T}=\left (\frac{\partial S}{\partial V} \right )_{S,N}$

Answer 1

(11 TOS du Pov volume = curt TOS = 8 Td - (VOT (= T/ds OT v 2 TU- oh - VOP At lurtant prenure ap=0 TO = Oh = (pur T DJ 6 IT Cum premibility Bulk malulus Bm - Direct strain volumetric stron BM - - de ov VOP ov -1 Isothermal comprensibility : I'm प KI --- ov JP To establish Cp (u= TV ² ki

Cror & I dv JT (por - Trov 0p (p dT - IVOT - T avtT D UT (ep-lular o T ( 1), N 77(4), AP dT : I (OP) dut I (p-( f) te T = CIT TO I= F(pv) use portial dift OP HOT UP dr cumpure cocht of ov T OT Ср - (p-v=I OP UV Or JT/P T = F (PV) lov UP/ OP 02 EUR ov ork ОТ /р (pl: TT), y lp (p- lv = -T

Cp - lu = -T B² v² ) x 8 (p-10 = Tup? 2 (p = (v + TVP2

Please find the work above. CP CV and KT and the final expression evaluated.