1. (a) Write the total differentials of s-S(V, T),S- S(P, T). Get used to it. This...
By considering the volume V and entropy S as the two independent variables in the thermodynamic equation dE = TdS−PdV , derive the Maxwell relation between the derivatives ∂T/ ∂V and ∂P/ ∂S .
Many times it is useful re-writing partial differential thermodynamic expressions in different forms using the total differentials for E, H, F. and G. The total differentials of E, H, F, and G are: dE = TDS – PdV + udn dH = TDS + VDP + udn dF = -SDT – PdV + udn dG = -SDT + VdP + udn - Part A Rewrite the following expression in terms of S, T, P, V.1, 11, Q, CAm, and/or Cvm,...
4. (25 pts) The Gibb's free energy of a system of N particles is given by, G(T,p)=-Nk T In“- (a) dG = ? (write in differential form similar to dU = TDS - pdV) (b) Find expressions for S and V written as partial derivatives with respect to G. (c) Compute the constant pressure heat capacity Cp of the system: C=T(dS/dT), Hint: Use your expression for S derived in (b) above, 3333333 (d) Extract the equation of state for this...
02) Consider a hydrostatic system represented by the thermodynamic variables volume V, pressure P and temperature T. a) Consider entropy S = S(T, V) and derive the equation TdS. Tas = Cvat +T (1) dV. V Show that this equation can be written as follows BT TdS = CydT + PDV where Cv is the thermal capacity at constant volume, B is the isobaric expansiveness and K is isothermal compressibility: b) Consider a gas described by the equation of state...
The Sackur-Tetrode Equation gives the entropy of a sample of n moles of monatomic ideal gas as a function of its internal energy U and volume V S(U, V) = 5/2 n R + n R In (V/n N_A(4piM U/3nN^2_Ah^2)^3/2) In the equation, R is the gas constant, M is the molar mass, N_4 is Avogadro's number, and h is Plank's constant. The equation can be derived using S = k ln W and directly computing W, the number of...
Represent in coordinates p-v and T-s the transformation for which a system receives heat but lowers its temperature. Explain why this is possible.
The amount of heat needed to raise the temperature of 1 mole of a substance by one Celsius degree (or, equivalently, one kelvin) is called the molar heat capacity of the system, denoted by the letter C. If a small amount of heat dQ is put into n moles of a substance, and the resulting change in temperature for the system is dT, then C=1ndQdT. This is the definition of molar heat capacity--the amount of heat Q added per infinitesimal...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or black body) radiation in terms of the energy per unit volume u. (a) An ideal quantum gas comprises non-interacting identical particles with discrete quantum states labelled 1, 2, ...,r ,....The partition function is given by Z (T,V,N)- > exp(-B(n,&, + п,&, +...)} пп. (i) Define the symbols n1, n2,...,n,...and 81, 82, ..., Er,... (iiExplain why, for photons, the partition function may be expressed as:...
An isolated system contains an ideal gas with state parameters: U, T, S, P, V, M, N. (vii) (viii) Describe an irreversible process that increases both the internal energy of the system, U, and the entropy of the system, S. Calculate the increase in entropy that results from the process you have chosen. What is the source of the increase entropy in this process? (ix)
deal gases obey the equation PV nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, T is its temperature, and the constant R-8.314 KPa-liters-mol-1 kelvin-1 (a) Find the exac t change in volume of O, gas as the pressure increases from 12.00 to 12.01 KPa, the temperature decreases from 300.0 to 299.9 degrees kelvin, and the number of moles of 0, gas changes from 1.03 to 1.01 moles....