Oregon State University Chemistry Exam 2 - Thermodynamics, Exams of Physical Chemistry

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Oregon State University, Department of Chemistry

Chemistry 440 Hour exam 2 , 16 November 2005

Name ..^ E r n M...............^ .......l e y..............

dE = dU(S,V ,ni) = TdS - PdV + xpidni

i

dH(S,P, ni) = TdS + V d P + xpidni

i

dA(T,V,ni) = -SdT - PdV + xpidni

i

dG(T,P, ni) = -SdT + V d P + xpidni

i

H = U + P V

A = U - T S

Pl Vy = %h7;T2/T1=^ ( V ~ / V ~ ) ~ - 'adiabatic process^ y^ =^ Cp/Cu

A H

coex

problem 1 A H / ( R T a )

3 \ n 2

1. (12 pts) One mole of water vapor at a temperature Ta is heated to temperature Tb =

2T,. What are the changes in entropy and enthalpy if a) the pressure is held constant; and b) the volume is held constant? Assume water vapor behaves as an ideal gas with

C, = 3R.

as = ~,,IR[Tz/-~;) = c p l n 2 = 4 ~ h 2 4 a* = C =^ 4 R ( 2 -TL) ~ ~ = 4 R L

2. ( 8 pts) Two blocks of iron of equal mass are placed in thermal contact and are allowed

t o equilibrate. Their initial temperatures are 27°C and 127°C. Derive AH, AS.

3. (12 pts) Shown is a plot of P vs T for a single component system.

(a) Label the liquid, gas and solid phases on the figure.

(b) Derive the coexistence temperature at Tbif the pressure is increased from that at

point a to that a t point b.

(c) Plot p(T, P) vs T for a pressure where liquid, solid and gas phases can exist.

Label the graph according to the phases that exist.

4. (12 pts) It is proposed that the Gibbs energy of a material a t pressure P and temper-

ature T is given by

where a, b, c are constants. Derive:

(a) the density as a function of pressure (b) the entropy, (c) and determine if the third law is obeyed for this material.

5. (8 pts) Circle all the correct responses from the list of equalities.

where the T , P, E, V subscripts denote variables held constant.

6. (8 pts) (a) Name two thermodynamic properties that diverge a t a second order tran- sition? KT CQ and (b) two quantities that change discontinuously a t a first order transition? , H,, S

7. (40 pts) Derive the following identities using as a starting point any of the relations

given on page I.

( ) = some function of QP