se dp +| dS = se dT Use (ƏS/ƏT), = C,/T and an appropriate Maxwell relation to show that TdS = C,dT- aTVdp, where the expansion coefficient, a, is defined as a= (1/V)(av/ƏT),. Hence, show that the energy transferred as heat, q, when the pressure on an incompressible liquid or solid is increased by Ap in a reversible isothermal process is given by q = -aTVAp. Evaluate q when the pressure acting on 100 cm' of mercury at 0°C is increased by 1.0 kbar. (a= 1.82 × 10*K'.) P3E.6 Suppose that S is regarded as a function of p and T so that

se dp +| dS = se dT Use (ƏS/ƏT), = C,/T and an appropriate Maxwell relation to show that TdS = C,dT- aTVdp, where the expansion coefficient, a, is defined as a= (1/V)(av/ƏT),. Hence, show that the energy transferred as heat, q, when the pressure on an incompressible liquid or solid is increased by Ap in a reversible isothermal process is given by q = -aTVAp. Evaluate q when the pressure acting on 100 cm' of mercury at 0°C is increased by 1.0 kbar. (a= 1.82 × 10*K'.) P3E.6 Suppose that S is regarded as a function of p and T so that

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter1: Gases And The Zeroth Law Of Thermodynamics

Section: Chapter Questions

Problem 1.65E: Determine an expression for V/T p, n in terms of and . Does the sign on the expression make sense...

See similar textbooks

Similar questions

(3A) Calculate the Gibbs free energy of mixing for 50.0 g water and 50.0 g ethanol at constant 298 K and1.00 bar. What is it about your answer that tells vou that this mixing is spontaneous?AmixG = NRT (x1 In x1 + x2 In x2)
3. One mole of liquid water at 100 °C is heated until the liquid is converted entirely to vapor at 100 °C and 1 atm pressure. Calculate q, w, AE and AH for each of the following. (a) The vaporization is carried out in a cylinder where the external pressure on the piston is maintained at 1 atm throughout. (b) The cylinder is first expanded against vacuum (Pext = 0) to the same volume as in part (a), and then sufficient heat is added to vaporize the liquid completely to 1 atm pressure.
(2) The Gibbs function G is (GF) ₁ P == ound ·S (06), = relationship (25) a = -(=++) ₂ thu modynamic property. If =V, prove the following
Determine Z and V for steam (H2O) at 250 °C (523.15 K) and 1800 kPa by the following: (a) Ideal gas equation (b) The truncated virial equation, Z=P/V=1+B/V+C/V^2, with the following experimental values of virial coefficients: B = 152.5cm^3/mol; C = -5800cm^6/mol (c) Truncated virial equation up to the parameter B (C excluded). (d) The steam tables (e) Soave/Redlich/Kwong equation (f) Peng/Robinson equation (g) Generalized Pitzer Correlation
The atomic heat capacity of solid Mo is given by the equation 0.503 x 105 Cp = 5.69 + 1.88 x 10-3 T – T² Find the change in entropy (in eu) which accompanies the heating of one mole of Mo from o C to its melting point, 2620°C. (Entropy unit, (eu) equal to i cal K-¹). Cp expression gives heat capacity in units of cal/mol.
Derive the following thermodynamic equation of state. ne = -P + T av Apply the equation to the following. (a) an ideal gas (b) a van der Waals gas Comment on your results. Step 1 of 7 Derive the following thermodynamic equation of state. (), au = -P + T IT av aT V Differentiate the equation dU = –PdV + TdS with respect to V while keeping T constant to obtain an () as expression for Use the following as necessary: P, S, T, V, and ASV¡ to represent av IT av au nRT av V -P+T·ASVT Step 2 of 7 (), and (), (ux Identify the relationship between Use the following as necessary: P, S, T, V, and APTV to represent as
The Gibbs Function G is a thermodynamic property. If following relationship as Ꮩ . (ap)T = -(T)P p=-S and = V, prove the
P2D.2 Starting from the expression Cp − CV = T(∂p/∂T)V(∂V/∂T)p, use theappropriate relations between partial derivatives (The chemist’s toolkit 9 inTopic 2A) to show thatC CT V TV p( / )( / ) p VpT
(a) For an ideal gas equation of state, prove that P P P dP = dn +=dT dv n (b) Suppose 1.000 mol of ideal gas at 300.0 K in a 30.00 L vessel increased in volume by 0.050 L. Use your answer from part (a) to compute the change in the pressure AP. (c) Compare to the exact change in pressure using the ideal gas equation of state to the estimate given by AP.
the ionic compound L2O3(s) is the ionic compound formed from oxygen and a metal with the form L(s) at 1.00 bar and 298 K. (a) Draw the Lewis structure for L2O3. Assume that all the valence electrons from L are required. (b) Use the following information to determine the enthalpy of formation for L2O3(s). Express your answer in kJZ(mol L2O3(s)). Lattice energy for L2O3(s) = -14836 kJ mol1 AHsub for L(s) = 358 kJ mol 1 First ionization energy for L(g) = 577 kJ mol 1 Second ionization energy for L(g) = 1794 kJ mol 1 Third ionization energy for L(g) = 3820 kJ mol 1 Bond dissociation energy for O2(g) = 498 kJ mol 1 %3D First electron affinity for O = -141 kJ mol 1 Second electron affinity for O = 744 kJ mol 1
A7. (a) Given that for an ideal gas (0) AG=nRT In aG ap =V, show that for a change in pressure from P₁ to P₂ ompression of two
The differential for the Gibbs function, G, at constant composition is: ?G = −S?T + Vdp Using the criterion for exact differentials, write the Maxwell relation that is derived from this equation.