Question

In: Other

(a) Starting from entropy as a function of pressure and volume, S(P, V), show that d...

(a) Starting from entropy as a function of pressure and volume, S(P, V), show that

d S = C V T ( ∂ T ∂ P ) V d P + C P T ( ∂ T ∂ V ) P d V

For a certain gas that follows the following equation of state:

P(V-b) = RT

Where b is a constant

(b) Starting from the above relationship show that P(V-b)γ=constant for the reversible adiabatic process. Assume constant heat capacity and γ=CP/CV as that for the ideal gas.

Solutions

Expert Solution


Related Solutions

Starting with the exact differential for S (entropy, treated as a state function of P, pressure,...
Starting with the exact differential for S (entropy, treated as a state function of P, pressure, and T, temperature), the definition of entropy, S, definition of heat, q, and the definition of enthalpy, H, show that dS= (Cp/T)dT - alpha*V*dP where alpha= (1/V)*(dV/dT) when P is held constant .Using the Helmholtz free energy, A, given by A=U - TS express dS in terms of dT and dV
The pressure p and volume v of a given mass of gas are connected by the...
The pressure p and volume v of a given mass of gas are connected by the relation k=(p+a\v^2)(v-b) where a, b, and k are constants. Using the composite trapezoidal method, write a MatLab script to approximate the work done by the gas in expanding from an initial volume to a final volume. Express p in terms of v. Where W = Integral (Pdv)
Derive the following statement "T(temperatue)-V(volume) and P(pressure)-V(volume) relationship in the adiabatic changes"
Derive the following statement "T(temperatue)-V(volume) and P(pressure)-V(volume) relationship in the adiabatic changes"
Using the relationship for internal pressure πT = T (∂P/∂T)V – P, show that for a...
Using the relationship for internal pressure πT = T (∂P/∂T)V – P, show that for a gas that obeys a truncated virial equation of state: Z = PVm/RT = 1 + B(T)/Vm, the internal pressure may be approximated as πT ≈ RT2(Vm)-2∙(ΔB/ΔT). Estimate the internal pressure at 1.0 bar and also at 10.0 bar for a hypothetical real gas at 275K given that B(T) = -28.0 cm3⋅mol-1 at 250K and -15.6 cm3⋅mol-1 at 300K for this gas.
Show that Cp = T(∂S/∂T)p and Cv = T(∂S/∂T)V
Show that Cp = T(∂S/∂T)p and Cv = T(∂S/∂T)V
Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p) ⊕ (p...
Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p) ⊕ (p v ~q) is equivalent to p v q. v = or, ~ = not, ⊕ = exclusive or (XOR). Please show the steps with the name of the law beside each step, thanks so much!
The ideal gas law PV=nRT relates pressure P, volume V, temperature T, and number of moles...
The ideal gas law PV=nRT relates pressure P, volume V, temperature T, and number of moles of a gas, n. The gas constant R equals 0.08206 L⋅atm/(K⋅mol) or 8.3145 J/(K⋅mol). The equation can be rearranged as follows to solve for n: n=PVRT This equation is useful when dealing with gaseous reactions because stoichiometric calculations involve mole ratios. Part A When heated, calcium carbonate decomposes to yield calcium oxide and carbon dioxide gas via the reaction CaCO3(s)→CaO(s)+CO2(g) What is the mass...
Let p be a prime and d a divisor of p-1. show that the d th...
Let p be a prime and d a divisor of p-1. show that the d th powers form a subgroup of U(Z/pZ) of order (p-1)/d. Calculate this subgroup for p=11, d=5; p=17,d=4 ;p=19,d=6
starting from A=-kTlnZ. Derive the statistical mechanical formulas for S,P,U
starting from A=-kTlnZ. Derive the statistical mechanical formulas for S,P,U
1. Starting from the enzyme-catalyzed reaction: S -> P Derive the (a) Michaelis-Menten Equation (b) starting...
1. Starting from the enzyme-catalyzed reaction: S -> P Derive the (a) Michaelis-Menten Equation (b) starting from the Michaelis-Menten equation, derive the Lineweaver-Burker plot. Provide brief explanation in each step. 2. Predict the optimum pH and temperature for human saliat amylase. Why did you arrive on the prediction?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT