Question

The isobaric thermal expansivity ? is defined as ? = 1 ? (?? ?? ) ?...

The isobaric thermal expansivity ? is defined as ? = 1 ?
(?? ??
)
?

The isothermal compressibility ? is defined as ? = −1 ?
(?? ??
)
?


1. From ? = ?(?,?), show that ?? = ???? −????
2. From ? = ?(?,?), show that ?? = ?? ?
?? −????
3. From ? = ?(?,?), show that ?? = (?? −???)?? +?(?? −??)??
4. From ? = ?(?,?), show that ?? = ???? +?(1−??)??
5. From ? = ?(?,?), show that ?? = −(?+???)?? +?????

Homework Answers

Answer #1

1)

Now write dV. This step is common for all the problem.

are the terms at constant pressure and constant temperature respectively.

since and , substitute for and in (2)

thus

Remaining questions can be solved in similar way by using Maxwell Relations.

Second step is common for all the problems. Compare and understand how it is written.

Please find attached the link to remaining solutions for this question.

https://drive.google.com/open?id=13T6HOEVYNx70E_Srsf6nS16l8EwRA76r

Have a good day!

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove for an isothermal isobaric system, the particles can only move from the region of higher...
Prove for an isothermal isobaric system, the particles can only move from the region of higher Gibbs free energy to the region of lower Gibss free energy,
21.3 moles of a diatomic ideal gas undergo three steps: A to B is an isobaric...
21.3 moles of a diatomic ideal gas undergo three steps: A to B is an isobaric (constant pressure P1 = 4.15x106 Pascal) expansion from volume V1 = 0.0609 m3 to V2 = 0.934 m3. B to C is isochoric (constant volume) C to A is isothermal (constant T). During the isobaric expansion from A to B: find Q, the heat transferred, in Joules. Give your answer in scientific notation. NOTE: A positive sign means heat has been added; a negative...
The following data are available for liquid ethanol at 20 C: M.W. = 46.07, Density =...
The following data are available for liquid ethanol at 20 C: M.W. = 46.07, Density = 0.7893 g/cc, Coefficient of thermal expansion = 1.12x10^-3 K^-1, Isothermal compressibility = 1.0x10^-4 bar^-1 (a) Estimate the difference (Cp-Cv) for liquid ethanol at 20 C in J/mol K (b) 10 liters of liquid ethanol at 20 C is compressed isothermally from initial pressure of 1 bar to a final pressure of 50 bar. For this process, calculate the enthalpy and entropy change of the...
A Student cycle engine is analyzed using the cold air-standard method. Given the definition of each...
A Student cycle engine is analyzed using the cold air-standard method. Given the definition of each process in the cycle, determine the thermal efficiency of the engine for each set of defined ratios listed below. All ratios are given as the larger value over the smaller one. --Given Values-- Process 1-2 = Isentropic compression & volume ratio=rv12 Process 2-3 = Isothermal compression & volume ratio=rv23 Process 3-4 = Isobaric heat addition & temperature ratio=rT34 Process 4-5 = Isometric heat addition...
. Dr. Hu has made some biocompatible prosthetics out of silk. The final processing step requires...
. Dr. Hu has made some biocompatible prosthetics out of silk. The final processing step requires high pressure to remove any pores. The pressure on 1 kg of silk at room temperature is isothermally increased from 1 atmosphere to 100 atmospheres. The volumetric thermal expansion is -4.0×10-5/K, the isothermal compressibility is 2×10-10/Pa, and the heat capacity is 2000 J/K. a)What was the work done? b)What was the change in heat? c)What would be the temperature change if this was done...
4. Consider the function ?(?) = ? + 1 ? − 2 Defined for ? >...
4. Consider the function ?(?) = ? + 1 ? − 2 Defined for ? > 0. First, show that this function has one global minimum at ? = 1. Then, take the Taylor series expansion about the point ? = 1, writing ? = 1 + ?. Compute the terms out to ? 3 .
A table of values is given for a function f(x, y) defined on R = [1,...
A table of values is given for a function f(x, y) defined on R = [1, 3] × [0, 4]. 0 1 2 3 4 1.0 2 0 -3 -6 -5 1.5 3 1 -4 -5 -6 2.0 4 3 0 -5 -8 2.5 5 4 3 -1 -4 3.0 7 8 6 3 0 Estimate f(x, y) dA R using the Midpoint Rule with m = n = 2 and estimate the double integral with m = n =...
Rod 1, with a thermal conductivity of 373 W/m·K, rod 2, with a thermal conductivity of...
Rod 1, with a thermal conductivity of 373 W/m·K, rod 2, with a thermal conductivity of 292 W/m·K, and rod 3, with a thermal conductivity of 112 W/m·K, are placed end to end with rod 2 between the other two. The rods have the same length and the same diameter. The free end of rod 1 is maintained at water's boiling point, and the free end of rod 3 is maintained at water's freezing point. What is the steady-state temperature...
1.The spot rate of interest is defined by s(t) = .1(.9)t for t = 1, 2,...
1.The spot rate of interest is defined by s(t) = .1(.9)t for t = 1, 2, 3, 4, 5. Find the present value of a 5-year annuity-due in which the first payment is equal to $1000, and each subsequent payment increases by 5% of the immediately preceding payment. 2.You are given the following term structure of spot interest rates: Term (in years) Spot interest rate 1 5% 2 5.75% 3 6.25% 4 6.50% A three-year annuity-immediate will be issued a...
Why are plasticizers added to polymers? Choose one or more: 1.         To improve thermal stability. 2.        ...
Why are plasticizers added to polymers? Choose one or more: 1.         To improve thermal stability. 2.         To improve flexibility. 3.         To improve toughness. 4.         To improve tensile strength. 5.         To improve compressive strength.