A metal rod of length 20 cm and diameter 1 cm is covered with non-conducting substance. One of its end is maintained at 100°C, while the other end is put in ice at 0°C. It is found that 25 gm of ice melts in 5 minutes . Calculate the co-efficient of thermal conductivity of the metal in cm-1°C-1S-1. [ specific latent heat of ice : 80 cal/g/°C]

Question

A metal rod of length 20 cm and diameter 1 cm is covered with non-conducting substance. One of its end is maintained at 100°C,  while the other end is put in ice at 0°C. It is found that 25 gm of ice melts in 5 minutes . Calculate the co-efficient of thermal conductivity of the metal in cm-1°C-1S-1. [ specific latent heat of ice : 80 cal/g/°C]

Accepted Answer

ক. 1.697

ব্যাখ্যা: তাপ পরিবহনের সূত্র অনুযায়ী, $Q = \frac{K A (	heta_1 - 	heta_2) t}{L} \implies K = \frac{Q L}{A (	heta_1 - 	heta_2) t}$।
এখানে,
বরফ গলতে প্রয়োজনীয় তাপ, $Q = m L_f = 25	ext{ g} 	imes 80	ext{ cal/g} = 2000	ext{ cal}$
দৈর্ঘ্য, $L = 20	ext{ cm}$
ব্যাস $d = 1	ext{ cm} \implies$ ব্যাসার্ধ $r = 0.5	ext{ cm}$
প্রস্থচ্ছেদের ক্ষেত্রফল, $A = \pi r^2 = \pi (0.5)^2 = \frac{\pi}{4}	ext{ cm}^2$
তাপমাত্রার পার্থক্য, $\Delta 	heta = 100 - 0 = 100^\circ	ext{C}$
সময়, $t = 5	ext{ min} = 300	ext{ s}$
অতএব,
$K = \frac{2000 	imes 20}{\frac{\pi}{4} 	imes 100 	imes 300} = \frac{40000}{30000 	imes \frac{\pi}{4}} = \frac{16}{3\pi} \approx 1.697	ext{ cal}\cdot	ext{cm}^{-1}\cdot^\circ	ext{C}^{-1}\cdot	ext{s}^{-1}$।

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