A rod of negligible heat capacity has length 20 cm, area of cross-section 1.0 cm2 and thermal conductivity 200 W/m-°C. The temperature of one end is maintained at 0°C and that of the other end if slowly and linearly varied from 0°C to 60°C in 10 minutes. Assuming no loss of heat through the sides, find the total heat transmitted through the rod in these 10 minutes.

Sol. The temp at the both ends of bar F is same Rate of Heat flow to right = Rate of heat flow through left ⇒ (Q/t) base A + (Q/t) base C = (Q/t) base B + (Q/t) base D ⇒ K base A(T base 1 - T)A/l + K base C(T base 1 - T)A/l = K base B(T - T – base 2)/l + K base D(T - T – base 2)A/l ⇒ 2K base 0(T base 1 - T) = 2 * K base 0(T – T base 0) ⇒ T base 1 – T = 2T – 2T base 2 ⇒ T = T base 1 + 2T base 2/3