Molten lead of mass `m = 5.0 g` at a temperature `t_2 = 327^@C` (the melting temperature of lead) was poured into a calorimeter packed with a large amount of ice at a temperature `t_1 = 0 ^@C`. Find the entropy increment of the system lead-ice by the moment the thermal equilibrium is reached. The specific latent heat of melting of lead is equal to `q = 22.5 J//g` and its specific heat capacity is equal to `c = 0.125 J//(g.K)`.

Explanation

`Delta S = -(m q_1)/(T_2) - mc 1n (T_2)/(T_1) + (M q_(ice))/(T_1)`
where `M q_(ice) = m(q_2 + c(T_2 - T_1)`
=`mq_2 ((1)/(T_1) -(1)/(T_2)) + mc ((T_2)/(T_1) - 1 -(T_2)/(T_1))`
=`0.2245 + 0.2564 ~~ 0.48 J//K`.