Honors Solutions to Chapt 14

Here are solutions to Chapt 14 prob 31, 39, 42, 65 both via link and included here ( but all symbols and exponents are messed up so use the link if you can)

http://h1.ripway.com/DrCherdack/Solutions%20to%20Giancoli%20Cha.doc



Solutions to Giancoli Chapter 14

31. Qin = ΔU Lf ΔM where Lf is the heat of fusion ( i.e. the energy it takes to melt one kg.) and DM is the mass melted.

DM = Qin/Lf but Qin = 0.50 x |ΔKE| = .50 Mvinitial 2/2 = 0.50 x 54 x6.42/2= 553 J and Lf = 3.34E5 so ΔM = 5.53E2/3.34E5 = 1.66 E-3 kg.

39. heat flow through the copper = heat flow through the copper = heat flow through the aluminum = total heat flow so
= ΔTcopper kthermal conductivity of copper A/L = ΔTaluminum kthermal conductivity of aluminum A/L
ΔTcopper = 250 –T and ΔTaluminum = T-0 the As and Ls cancel so we have

(250 –T)kthermal conductivity of copper = T kthermal conductivity of aluminum

gathering terms in T to the right side we have

250 kthermal conductivity of copper = T(kthermal conductivity of copper + kthermal conductivity of aluminum)

or T = 250 kthermal conductivity of copper / (kthermal conductivity of copper + kthermal conductivity of aluminum).

42. Using notes on thermal conductance I provided I have R equiv = R1 +R2.

ΔQ/Δt = (Thot-Tcool) xA x k/L = (Thot-Tcool)/R . However the book uses R differently from me and I should have warned you. The book uses R as resistance for a wall with an area of one unit of area. Clearly the heat conductance of a wall is proportional to the area ( bigger area wall has more heat flowing through it) and since resistance is simply 1/conductance, the resistance ( R as I use it) goes as 1/area. So the R-19 which is in US units needs to be divided by the 240 square feet to get the R as I use it.


Thus we have Rbook for brick is about 1 ( page 397) and for the insulation Rbook is about 19 for a total of 20. Dividing this by the area gives an RCherdack of 1/12 (deg F hr/Btu).

So ΔQ/Δt = 12F /(1/12) =144 Btu/hr or .27 J/s [1Btu = 1050 J; 1 sec =1/3600 hr].

65. Q = McΔT= 185 kg x4186x40; Δt = Q/Power, since power is energy /Δt