Question

A 25 g piece of an unknown metal alloy at 150°C is dropped into an insulated container with 200 g of ice. How do you calculate the specific heat capacity of the metal, given that 9.0 g of ice melted?

Answer 1

You never gave us the temperature of the ice, so I will assume it's approximately `0°C`.

Moreover, we'll need the enthalpy of fusion for water,

`DeltaH_("fus") approx (6.0kJ)/(mol)`

Let's figure out how much heat was used to melt that ice,

`9.0g * (mol)/(18g) * (6.0kJ)/(mol) approx 3.0kJ`

Moreover, let's assume that the metal only released that heat and equilibrated with the ice,

`3000J = 25g * C_s * 150°C`

`therefore C_s approx (0.8J)/(g*°C)`

This is fairly reasonable, most metals' specific heats are between 0 and 1. I'm open to feedback if I made a mistake!