The adiabatic thermal expansion coefficient is defined by the relation
αs=Cv/T(dV/dT)s.
(a) Evaluate αs in terms of α(expansivity), β(compressibility), Cv,
T, and V.
(b) Show that αs=-Cv/nRT for an ideal gas.
The adiabatic thermal expansion coefficient is defined by the relation αs=Cv/T(dV/dT)s. (a) Evaluate αs in terms...
Calculate the isothermal compressibility and the expansion coefficient of a perfect gas and a van der Waals ga:s (ii) Show, using Euler's chain relation, that KTR α(Vin-b) (iii) Make use of the definitions of the coefficient of thermal expansion, α, and 1. (i) (15) the isothermal compressibility, KT, and start from the expression for the total differential dV in terms of T and P to show that: OT
Let S = V-1 (V/T)S be the isoentropic coefficient of thermal expansion. Use a Maxwell relation and the expansion, chain and inversion relationships to show that S = - CV/VT
2 Calculate the isobanic volumetric thermal expansion coefficient and the isothermal Compressibility, respectively, defined by 2=+2), k ept for an ideal gas at 298K and 1.00 bar L.
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1) The volume thermal expansion coefficient is defined as the fractional change in volume of a substance per unit change in temperature. Consider a closed chamber containing a monatomic ideal gas at atmospheric pressure. Consider its behavior as its temperature is increased by a small amount T, and find its volume expansion coefficient, assuming (a) isobaric and (b) adiabatic conditions. Finally, (c) discuss why these two values are different, and compare them to expansion coefficients of liquids and solids.
HW PROBLEM 5. Consider the isentropic compression/expansion of an ideal gas in a closed system defined by the inside volume of a frictionless piston. Let and denoted the molar specific heats of the ideal gas at constant volume and pressure, respectively and let the adiabatic coefficient by defined as Derive the following relationships, and in each case give a formula for the variable indicated as "constant" a) T VG = constant b) 0,* P1 = constant c) P(V") = constant
2. For the Berthelot Equation of State (see #5 on Phy 372 home page): (a) Expand P in terms of v and T, i.e. start with dP and express it in terms of dv and dT. (Here v is the molar specific volume.) Rewrite the expansion with the coefficients evaluated. These coefficients will be functions of v and (b) Ú (c) Write an expression for β. The result will again be a function of v and se the cyclic relation...
Problem I (40 pts): Simplify and evaluate the following thermodynamic quantities for an ideal gas (assuming n-1.0 mole, T-300 K, and P-0.1 MPa). a) (10 pts) The Joule-Thompson coefficient (1) ar ОР V(Tap-1) H b) (10 pts) The isobaric thermal expansion coefficient (AP) c) (10 pts) The isothermal compressibility (KT) d) (10 pts) The heat capacity at constant pressure (C)
only 6...7...and 8
The Gibbs function of a thermodynamic system is defined by G H- TS. If the system is consisting of two phases 1 and 2 of a single substance and maintained at a constant temperature and pressure, the equilibriunm condition for the coexistence of these two phases is that the specific Gibbs functions are equal Consider now a first-order phase change between the phase 1 and the phase 2. At the phase boundary, the equilibrium condition for the...
The solution belongs to the 1st question, i need the solution
for the 2nd question.
1. A single cylinder 1.6 lt, spark ignition engine is operating on the ideal Otto cycle at a compression ratio of 9. The ambient air around the engine is at 1 bar and 20 °C and the fuel consumption of the engine is 13 L/h gasoline at 5600 rpm. Evaluate a. The highest pressure and temperature in the cylinder throughout the cycle b. Net work...
10. Given the following table: Compound NO: (g) N:O (g) AHP (J mol) AGP (J mol) 51.84 33.85 9.66 98.29 For the reaction: N:Oa (g) eo 2NO: (g) (a) Use the information in the Table to calculate AG for the reaction (b) Use the information in the Table to calculate AH" for the reaction (c) Calculate K, at 25 C. (d) Calculate K, at 1600 °C. (Assume AH to be temperature independent) (e) Calculate the degree of dissociation, a, of...