Question

One end of a uniform well-lagged metal bar of length 0.80 m and cross-sectional area of
4.0 x 10-3m2
is kept in steam at 100 ˚C while the other end is in melting ice in a well-lagged
container. The ice melts at a steady rate of 5.5 x 10- 4
kgs-1
and the thermal conductivity of
the material of the bar is 401 Wm-1K
-1
. Calculate the specific latent heat of fusion of ice

Answer 1

Solution.

$l=0.8m;$

$A=4.0\sdot10^{-3}m^2;$

$\Delta T=100K;$

$\dfrac{m}{t}=5.5\sdot10^{-4}kgs^{-1};$

$K=401Js^{-1}m^{-1}K^{-1};$

$\dfrac{\Delta Q}{\Delta t}=(\dfrac{m}{t})L_f\implies L_f=\dfrac{\dfrac{\Delta Q}{\Delta t}}{\dfrac{m}{t}};$

$\dfrac{\Delta Q}{\Delta t}=\dfrac{\Delta T}{l}\sdot K\sdot A;$

$\dfrac{\Delta Q}{\Delta t}=\dfrac{100K}{0.8m}\sdot401Js^{-1}m^{-1}K^{-1}\sdot 4.0\sdot 10^{-3}m^2=$ $200.5Js^{-1};$

$L_f=\dfrac{200.5Js^{-1}}{5.5\sdot10^{-4}kgs^{-1}}=3.65\sdot10^5Jkg^{-1};$

Answer: $L_f=3.65\sdot10^5Jkg^{-1}.$