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Question

One end of a lagged cylindrical metal rod of length 31.4 cm and radius 2 cm is kept in contact with ice at 0c and the other end in water at 100C. Find the rate of melting of ice per minute. L=80 cal/g,k=105 S.I. units (7.5 g).

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Solution

Given: One end of a lagged cylindrical metal rod of length 31.4 cm and radius 2 cm is kept in contact with ice at 0c and the other end in water at 100C.
To find the rate of melting of ice per minute.
Solution:
As per the given condition,
Length of the rod, l=31.4cm=0.314m
radius of the rod, r=2cm=0.02m
Area of cross section,A=4πr2=4×π×(0.02)2=5×103m2
Thermal coefficient, $k=10^5W/(mK)
Temperature difference between two ends of the rod (T1T2)=(1000)=100
time, t=1min=60s
If dQdt is the rate of melting of ice per minute, then
We know,
dQdt=KAt(T1T2)ldQdt=105×5×103×60×100)0.314dQdt=955×104J/s
is the rate of melting of ice per minute.

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