Question

One end of a uniform well lagged metal bar of length 0.8m and crossectional area of 4.0×10^-3m^2 is kept in steam at 100°c while the other end is melting in a well lagged container.The ice melt at a steady rate 5.5×10^-4KGS^-1 and the thermal conductivity of material of the bar is 401Am^-1k^-1.calculate the specific latent heat of fusion of ice

Answer 1

Solution.

$l=0.8m;$

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

$\Delta T=100^oC=100K;$

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

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

$L_f-?;$

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

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

$\dfrac{\Delta Q}{\Delta t}=\dfrac{100K}{0.8m}\sdot401Js^{-1}m^{-1}K^{-1}\sdot4.0\sdot10^{-3}m^2=200.5Js^{-1};$

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

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

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