Question

a)You are boiling pasta and absentmindedly grab a copper stirring spoon rather than your wooden spoon. The copper spoon has a 25 mmmm ×× 1.8 mmmm rectangular cross section, and the distance from the boiling water to your 35∘C∘C hand is 18 cmcm.How long does it take the spoon to transfer 35 JJ of energy to your hand?Express your answer with the appropriate units.

b)Your 300mL300mL cup of coffee is too hot to drink when served at 86.0 ∘C∘C.What is the mass of an ice cube, taken from a -21.0 ∘C∘C freezer, that will cool your coffee to a pleasant 65.0 ∘∘?Express your answer with the appropriate units.

Answer 1

PART (a):

We have:

Area of spoon, A = 25 x 1.8 x 10^-6 m² = 4.5 x 10^-5 m²

Thermal conductivity of copper, K = 400 W/m.K

Change in temperature, ΔT = 100 - 35 = 65^oC

Distance/thickness, x = 18 cm = 0.18 m

Heat transferred, Q = 35 J

Therefore, Time taken for the transfer is given by:

Q = (K.A.ΔT.t) / (x)

t = (Q.x) / (K.A.ΔT)

t = (35 x 0.18) / (400 x 4.5 x 10^-5 x 65)

t = 5.38 s ----------- (**Answer**)

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PART (b):

We have:

Mass of coffee = (300 mL) x (1 g/mL) = 300 g

Heat capacity of coffee = heat capacity of water = 4.184 J/g^oC

Let "m" be the mass of the ice required.

We know that, heat gained by ice = heat lost by the coffee

H_ice = H_coffee

(m.C_ice.ΔT ') + (L_f.m) + (m.C_w.ΔT ") = m_c.C_c.ΔT^o

(m x 2.09 x 21) + (334 x m) + (m x 4.184 x 65) = (300 x 4.184 x (86-65))

43.89 m + 334 m + 271.96 m = 26359.2

m (43.89 + 334 + 271.96) = 26359.2

m = (26359.2) / (649.85)

m = 40.56 g----------- (**Answer**)

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