# A container of negligible heat capacity contains 1kg of water. It is connected by a steel rod of length 10m and area of cross-section 10cm^(2) t

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A container of negligible heat capacity contains 1kg of water. It is connected by a steel rod of length 10m and area of cross-section 10cm^(2) to a large steam chamber which is maintained at 100^(@)C. If initial temperature of water is 0^(@)C, find the time after which it beomes 50^(@)C. (Neglect heat capacity of steel rod and assume no loss of heat to surroundings) (use table 3.1, take specific heat of water =4180 J//kg.^(@)C)

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Let temperature of water at time t be T, then thermal current at time t,
I = ((100 -T)/(R ))
This increases the temperature of water form T to T +dT
rArr i = (dH)/(dt) = ms (dT)/(dt)
rArr (100-T)/(R ) = ms(dT)/(dt) rArr overset(50)underset(0)int (dT)/(100-T) = overset(t)underset(0)int (dT)/(Rms)
rArr -ln ((1)/(2)) = (t)/(Rms)
or t = Rms ln2 sec
= (L)/(KA) ms ln2 sec
= ((10m)(1kg)(4180J//kg-^(@)C))/(46(w//m^(@)C)xx(10xx10^(-4)m^(2)))ln2
= (418)/(46) (0.69) xx 10^(5) = 6.27 xx 10^(5) sec = 174.16 hours