A well insulated box has two compartments A and B with a conducting wall between them. 100 g of ice at `0^(@)C` is kept in compartment A and 100 g of water at `100^(@)C` is kept in B at time t = 0. The temperature of the two parts A and B is monitored and a graph is plotted for temperatures `T_(A)` and `T_(B)` versus time (t) [Fig. (b)]. Assume that temperature inside each compartment remains uniform.

(a) Is it correct to assert that the conducting wall conducts heat at a uniform rate, irrespective of the temperature difference between A and B?
(b) Find the value of time `t_(1)` and temperature `T_(0)` shown in the graph, if it is known that `t_(0) = 200 s`.
Specific heat of ice `= 0.5 cal g^(-1) .^(@)C^(-1)`
Specific heat of water `= 1.0 cal g^(-1) .^(@)C^(-1)`
Latent heat of fusion of ice `= 80 cal g^(-1)`

Answer

(a) yes , (b) `T_(0) = 13.3^(@)C, t_(1) = 217 s`