Question

A bar 0.2m in length and 2.5 cm2 in cross section is ideally lagged. One end is maintained at 100° C and the other end is maintained at '0° C by immersing in melting ice. Calculate the mass of ice melt in one hour. Thermal conductivity of the material of the bar is 4x10-2 Wm-1 K-1 .​

Answer 1

The mass of ice melted is 529g.

Given that,

Length of the bar=0.2m

Area of cross section=2.5cm²=2.5×10^-4m²

Temperature at one end $t_{1}$= 100°C

Temperature at other end $t_{2}$=0°C

Time t= 1hr= 3600s

Thermal conductivity K= $4*10^{-2} Wm^{-1} K^{-1}$

We know,

Latent heat of ice=L=$3.4*10^{5}$

To find mass of ice melted in 1 hour,

The amount of heat produced Q,

Q=mL

Also,

Q=$\frac{KA(t_{2}-t_{2})t }{l}$

Therefore,

mL=$\frac{KA(t_{2}-t_{2})t }{l}$

m=$\frac{KA(t_{2}-t_{2})t }{lL}$

m=$\frac{4*10^{2} *2.5*10^{-4} (100-0)*3600}{0.2*3.4*10^{5} }$  

m=$\frac{3.6}{6.8 }$

m=$0.529 kg$

m=529g

Thus the mass of melted ice is 529g.

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