$1.$ Water of mass $62$ kg is contained in a silver vessel having a mass of $50\mathrm{.}3$ kg$.$ Both are at $95\backslash$deg C$.$ Ice of mass $35$ kg at $-19\backslash$deg C and $4\mathrm{.}5$ kg of dry steam at atmospheric pressure are also added. Determine the equilibrium temperature of the mixture.

$2.37$ kg of ice at $-32\backslash$deg C is put in a $22$ kg aluminum vessel which is at $25\backslash$deg C$,$ and $4$ kg of steam at $100\backslash$deg C is supplied. Determine how much ice and water remain by mass at thermal equilibrium.