show ALL work A 12.5 g of quartz at 1200 C is dropped into 2500 g of water at 20

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A 12.5 g of quartz at 1200 C is dropped into 2500 g of water at 20 C in an insulating container. (Look up specific heats of these substances). As a result, the temperature of water increases to T and the temperature of quartz decreases to T’ (a) Show that the entropy increase of the system is S = m1c1 ln(T/T1) + m2c2 ln (T’/T2) and (b) Show that energy conservation requires that m1c1(T - T1) = m2c2(T2 – T’) (c) Show that the entropy change considered as a function of T, is at maximum if it is at thermodynamic equilibrium. (d). Discuss the result of part (c) in terms of the idea of entropy as a measure of disorder.

Explanation / Answer

a) This is a calculation of an entropy change for an irreversible process. Since entropy is a state function, S is independent of path. All we have to do is imagine a reversible path which will effect the same change and calculate the entropy change for the reversibly path.

S_total = S_cold + S_hot

S_total = m1c1 integral T1 to T (dT/T) + m2c2 integral T2 to T' (dT/T)

S_total = m1c1 ln(T/T1) + m2c2 ln(T'/T2)

b) C = Q/dT

therefore m1(Q/dT)(T-T1)=m2(Q_2/dT)(T2-T')

c) you must get the total differential of S considered as a function of T (i.e. an equation of the form dS = f(T)dT +...

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