[Dolphinsiu]

I get stucked when I meet this question in test 2.

A cylinder with a piston was put in a water bath and at thermal equilibrium with the bath. The water bath contains 10 L water and 1 kg ice. The gas in the cylinder has a pressure of 1 atm and is being compressed isothermally and reversibly from 3 L to 0.8 L.

(a) Determine q, the heat transferred to the system of this process
q = - (1) 8.314 (298) ln (0.8/3) = 3274.7 J

(b) Determine the heat fusion of ice at 0 C
I leave blank as I don't know why I need to find, 334 J/kg is already known, right?

(c) Determine the changes in the amount of ice after the above process.
(What process is involved? If part (b) cannot be known how to find. Then I fail to do it and leave it blank)

(d) What is the Delta S(tot) of this process? What would the delta S(tot) be if the system is allowed to expand from 0.8 L back to 3L under a constant pressure (1 atm)?
(It seems the case is different as the previous process is isothermal, but still leave blank)

This question counts 40 marks. Perhap I only get 4 marks. So poor! Can anyone help me in Physical Chemistry and improve more in this kind of topics? I don't want to fail in the examination!

[Yggdrasil]

a)  How many moles of gas do you have (it's not 1)?  What temperature is the gas at (it's not 298K)?

b)  334 kJ/kg or equivalently 334 J/g.  I don't see how this could be derived from the information given.

c)  The system transfers heat to the surroundings and this heat melts ice.  Use the answers from (a) and (b) to figure out how much ice was melted.

d)  What is ΔS_tot for a reversible process?  What is ΔS_tot for an irreversible process?

[Dolphinsiu]

I know what you have said.

(a) T = PV/nR = (1)(3)/n (0.0821) = (36.54 / n) K
     q = -nRTln(V2/V1) = - 8.314 (36.54) ln (0.8/3) = 401.5 J

(b) H(latent) = 334 J/g

(c) 401.5 = 334 (m)
          m = 1.20 g

(d) ΔStot (rev) = - nR ln (V2/V1) + 334 (1.20) / 273
                     = - n (8.314) ln (0.8/3) + 401.5 / 273
                     = 10.99 n + 1.47

     T2 = PV/nR = 1 (0.8 ) / n (0.0821) = (9.74 / n) K

     Cp Δ T = 334 (m)
     75.291 (36.54 - 9.74 ) = 334 m
                              m = 6.04 kg

     ΔStot (irrev) = Cp ln (T1/T2) + H/T
                       = 75.291 ln (36.54/9.74) + 334 (6.04) / 273
                       = 106.9 kJ

Are my calculation right?

[enahs]

O th law of thermodynamics. If the Ice is in thermal equilibrium with the water, and the water is in thermal equilibrium with the piston, the piston is in thermal equilibrium with the ice.

You are still using n as one? You know everything but the amount of the gas, solve for that using your ideal gas law.

[Dolphinsiu]

I haven't used n as 1, but rather using T = (36.5/n) K

[Yggdrasil]

Your ice bath is at 0^oC = 273.15 K.  However, your calculations for parts (a) and (c) are correct, nonetheless.

For the first part of (d), you should be able to answer without any calculations.  Just remember the 2nd law of thermodynamics.  It is a conceptual question, not a computational one.  For calculating ΔS_tot for the irreversible process, however, you are doing something wrong as the units of entropy are J/K and you have units of energy (kJ). 

Remember that ΔS_sys is a state function, so it is not path-dependent.