Chapter 10 - Worked Solutions

to selected extension questions from the OUP text Senior Physics - Concepts in Context by Walding, Rapkins and Rossiter

Q 39.
A rating of 5 kW means it gives heat at the rate of 5 kJ per second
If we consider 1 minute:
5 kW = 5000 J s-1 = 5000 x 60 J min-1 = 300000 J min-1
In 1 minute 5 Kg of water pass through the shower unit.
Q = M c DT.
30000 = 5 x 4180 x DT
DT = 14.4 ^oC
The final temperature = 15 ^oC + 14.4 ^oC = 29.4 ^oC

Q 40
Assume that the heat lost from the iron goes into just melting the ice and does not raise its temperature
Q (lost) = Q (gained)
mcDT (iron) = mL_f(ice)
0.1 x 460 x (150 - 0) = m x 3.34 x 10⁵ 6900 = m x 3.34 x 10⁵ m = 0.0206 kg (= 20.6 g)
Density (D) = m/V
Density of ice at 0^oC is 0.9162 g/cm³
V = m/D = 20.6/0.9162 = 22.48 cm³Length of cylinder = Volume/Area = 22.48/(p r²)
L = 22.48/(p x 2²) = 1.79 cm (the answer in back of the book says 1.9 cm and this is wrong).
My thanks to Oscar Lee from St Joseph's College, Gregory Terrace, Brisbane for pointing out the error.
I'd normally send him a packet of Tim Tams but as they are made with palm oil I've stopped buying them. Sorry Oscar.

Q 41
Assume that the steam cools to 100°C, condenses to water at 100°C and then cools to 0°C. At the same time the ice cube melts and turns to water at 0°C
Q (lost) = Q (gained)
mcDT + mL_v + mcDT = mL_fm(2.02 x 10 + 2250 + 4.2 x 100) = 20 x 334
m = 2.48 g
\ m (total) = 55 g + 2.48 g = 57.48 g

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