CHEM360 Problem Set 4: Due July 11.

1. Consider a reversible isothermal expansion of two moles of CO2 from 1 L to 40 L at 300 K. Assume that

CO2 obeys an equation of state P = nRT/(V −nb)−n 2a/V 2 with b = .04286 L mol−1 and a = 3.658 L2 bar mol−2.

(a) Calculate the work W . (b) Use the formula (∂U∂V )n,T = −P + T ( ∂P ∂T )n,V to find ∆U . What is ∆H? (c) Use the

Maxwell Relation ( ∂S∂V )n,T = ( ∂P ∂T )n,V to find ∆S.

2. The coefficient of thermal expansion of water at 25 C is 2.572×10−4 K−1, and its isothermal compressibility

is 4.525×10−5 bar−1. Calculate the value of CP − CV for five moles of water at 25 C. The mass density of water at

25 C is .997 g mL−1.

3. A monatomic real gas has equation of state P = nRT/(V − nb) − n2a/[ √

TV (V + nb)].

(a) Find a formula for the internal energy U . [Hint: (∂U∂V )n,T = −P + T ( ∂P ∂T )n,V and 1/[V (V + nb)] = (1/nb)[1/V −

1/(V + nb)].]

(b) Find a formula for Cv using the result of (a).

4. In deriving the Maxwell relation for the internal energy U we assumed that U = U(n, S, V ). For a monatomic

ideal gas it can be shown that U = Ce2S/3nR/V 2/3 where C is a constant. Show that (∂U∂S )n,V = 2U/3nR and

( ∂U∂V )n,S = −2U/3V . Use U = 3nRT/2 and P = nRT/V to show that ( ∂U ∂S )n,V = T and (

∂U ∂V )n,S = −P .

5. The Gibbs free energy of benzene decreases continuously with temperature (at fixed pressure) and shows

three nearly linear segments corresponding to the solid, liquid and gas phases. The magnitude of the slopes

increases as one moves from solid to liquid, and liquid to gas. Use the formula (∂G∂T )n,P = −S to show that

S(gas) > S(liquid) > S(solid).

6. One mole of a monatomic ideal gas initially at a pressure of 2.5 bar with temperature 300 K is expanded to

a final pressure of 3.5 bar by a reversible path defined by P/V = constant. Calculate ∆U , Q, W and ∆H .

7. Use the Clausius-Clapeyron equation and ∆Hsub = ∆Hfus + ∆Hvap at the triple point to show that the slope of

the solid-gas P -T coexistence curve is greater than the slope of the liquid-gas coexistence c