7. a) Starting with the expression for heat added to a system: dq = Cydt +...
The 1st Law of Thermodynamics can be written in the differential form dQ dUPdV. i) By expressing dU in terms of dT and dV, show that dQ dV +P аT . dT (15 marks) Hence show that for one mole of an ideal gas, the heat capacities Cp and Cv differ by the Gas Constant, R (10 marks) TV B2 av Show that Cp-C can be also be expressed as Cp-C, -T| ӘР ат av к (15 marks) The 1st...
Please answer the question number 8. For a virial gas (to second order) this is not so obvious since: (partialdifferential E/partialdifferential V)_T = RT^2/V^2 dB/dT where B = B(T) is the second virial coefficient. Show that in order to be consistent with the second law of thermodynamics B(T) = g/T, where e, and g are constants. As you might know, the melting point of ice is 0 degree C. The heat capacity at constant pressure of ice is 37.8 J/mole-K,...
Example 4.6 The fugacity of a van der Waals gas Using the expression for the compressibility factor Z of a van der Waals gas given in equa- tion 1.26, what is the expression for fugacity of a van der Waals gas? As an approximation, terms in P2 and higher in the series expansion are omitted 2-1-0-(0)0r P RT RT Z In P dP P C'P 1 dP RTRT a b P a b RT RT 1Forfe-r a f P exp...
Q1 A useful relationship of partial differentiation in thermodynamics is (a )T㈜e㈜ 1 Try this relationship out on the van der Waals equation of state for a gas (P4詞(V-b)=RT Here P, V, and T are pressure, volume, and temperature. Q1 A useful relationship of partial differentiation in thermodynamics is (a )T㈜e㈜ 1 Try this relationship out on the van der Waals equation of state for a gas (P4詞(V-b)=RT Here P, V, and T are pressure, volume, and temperature.
physical chemistry 3. Derive formulas for AE, Aw, and Aq when a Van der Waal's gas undergoes: a) reversible isothermal expansion b) adiabatic expansion c) repeat steps a and b for an ideal gas d) Use the Maxwell relation derived from the Helmholtz free energy F =F(T,V) = -SdT PdV To prove that e) Determine for a Van der Waal's gas and an ideal gas. T()-P f) Explain the answer to part e in terms of the assumptions that define...
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...
4. 10 points A monoatomic gas obeys the van der Waals equation: N²a P= NT V - Nb V2 where N is the number of particles and a and b are known constants and t = kbT. The gas has a heat capacity Cy = 3N/2 in the limit V +0. a) Using the thermodynamic identities and the equation of state prove that acv = 0. av т (3 pts) b) Use the result of part a) to determine the...
(a) One mole of a monoatomic van der Waals gas obeys the equation of state A3. ) (V-b)=RT (p+ and its internal energy is expressed as U CvT where Cv is the molar isochoric heat capacity of an ideal gas. The gas is initially at pressure p and volume V (i) Explain the physical meaning of the parameters a and b in the equation of state of the gas (ii) Write down the equation that defines entropy in thermodynamics. Define...
P2: Comparison of EOS methods for gases Calculate the molar volume of n-butane at 510K and 25bar, using the (a) ideal-gas law, (b) the truncated virial equation, and 0 (c) the Pitzer correlation with the Lee-Kesler values for Z and Z For n-butane T 425.1 K, P 37.96 bar, w 0.2 P3: Comparison of cubic EOS Calculate V for sulfur hexafluoride at 75 C and 15 bar by the following equations: (a) The van der waals equation (b) The Redlich/Kwong...
11. A reversible heat engine uses a three-step cycle consisting of an isothermal expansion at temperature Ti, a constant volume cooling to temperature T2, and adiabatic compression back to the initial state. (a) Sketch the P-V diagram (b) If 1 mole of a van der Waals gas is used the working material, the efficiency of this engine is defined to be E = Suppose that the heat capacity of gas is independent of temperature. Show that the efficiency of the...