7.5 crn 120 C A cylindrical copper rod 37 cm long and 7.5 cm in diameter is plac

Question

7.5 crn 120 C A cylindrical copper rod 37 cm long and 7.5 cm in diameter is placed upright on a hot plate held at a constant temperature of 120° C, as indicated in the figure. A small depression on top of the rod holds an ice cube of mass m at an initial temperature of 0.0° C. It takes 25 s for the for the ice cube to completely melt, if no heat is lost to the surroundings. The thermal conductivity of copper is 390 W/(m C) (a) Assuming there is no heat loss through the vertical surface of the rod, how much heat is transferred to the ice cube during the melting process? (b) What is the mass of the ice cube?

Explanation / Answer

given

L = 37 cm = 0.37 m

d = 7.5 cm = 0.075 m

A = pi*d^2/4

= pi*0.075^2/4

= 0.00442 m^2

k = 390 W/(m C)

T2 = 120 C

T1 = 0 C

t = 25 s

a)
Amount of heat transfred,

Q = A*k*(T2 - T1)*t/L

= 0.00442*390*(120 - 0 )*25/0.37

= 1.40*10^4 J

b) let m is the mass of ice that is melting during 25s.

now use, Q = m*Lf

m = Q/Lf

= 1.40*10^4/(3.33*10^5)

= 0.042 kg or 42 grams

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