Hello, I've been looking through some books and done some examples. Unfortunately, they never give proper solutions. If anyone could help verify my responses, then it would be much appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

1.The Van der Waals constants for a gas are found to be a=10m^3.Pa/mol, and b=0.001m^3/mol. Calculate the critical temperature in K to the nearest degree.

RT(c)=8a/27b

T(c)=8*10 / 27*0.001*8.314 = 356K

2. At a pressure of p=2atm, the melting point of a material is T(m)=370K. The density of the solid phase is rho(s)=5400kg/m^3 and the density of the liquid phase is rho(l)=4500kg/m^3. If the pressure is changed to p=57atm, the fractional change in transition temperature is (deltaT)/T=0.045. Calculate the latent heat of fusion in kJ/kg to one decimal place.

(deltaP)/(deltaT) = (deltaH) / T(deltaV)

=> (deltaH) = (deltaP)T(deltaV)/(deltaT)

deltaP = 57-2 = 55atm = 55*101325Pa = 5572875Pa

deltaV = rho(l)^-1 - rho(s)^-1 = 1/27000 m^3/kg

deltaT = 0.045T = 0.045*370 = 16.65

.'. (deltaH) = 5572875*370/(16.65*27000) = 4586.7J/kg = 4.6kJ/kg

3. For a transition which occurs at a temperature of T(m) 150degrees C with a latent heat of 500kJ/mol, calculate the change in entropy in kJ/(mol.K) to one decimal place.

deltaS = deltaH/T = 500000/423 = 1.2kJ/(mol.K)

4. It is observed that at a particular temperature and pressure a mixture has 2 solid phases and 2 liquid phases in equilibrium. If the system is invariant at this temperature and pressure, calculate the number of components in the mixture.

F = C+2

Maximum degrees of freedom is 2+2 = 4

C = components

=> 4-2 = C

.'. C = 2

5. A bar of material is stretched from it's initial length of 3m to 3.001m. If the bar has a 5cm*5cm cross section, and it's Young's modulus is 7.6GPa, then assuming elastic behaviour, calculate the applied force to the nearest N.

Strain = Change in Length/ Initial Length = 0.001/3

Stress = Young's Modulus*Strain = 7.6e9 * 0.001/3 = 2533333.333.......

Force = Area*Stress = 0.05m*0.05m * 2533333.333.....

.'. F = 6333N

6. A cylindrical rod of diameter 1cm is stretched from it's initial length of 1.2m to a length of 1.23m. If the diameter of the bar is reduced to 0.9966cm, then assuming elastic behaviour, calculate Poisson's ratio for the material to 2 decimal places.

mu = poisson's ratio = - (strain in x)/(strain in z)

mu = -(change in diameter/diameter)/(change in length/length)

mu = -(-0.0034e-2/1e-2)/(0.03/1.2) = +0.136 = 0.14

7. A material has a bulk modulus of 56GPa and a Poisson's ratio of 0.27. Calculate Young's Modulus to the nearest GPa.

Bulk Modulus = K = Young's Modulus/(3-6mu)

Y = K(3-6mu) = 56e9(3-6(0.27)) = 77.3GPa = 77GPa

I have some more problems which I've done but I think that may be enough for now. I hope I have gotten these all right but sometimes I make stupid mistakes. Thanks in advance.

Levi.

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# Homework Help: Materials/Solid State Physics Problem Check.

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