heat lost by metal + heat gained by water = 0

[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0
Substitute and solve for specific heat metal.

I see you've typed my response to an earlier question but no question here.

To solve for the specific heat of the metal, we can use the equation:

[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0

Given that the equation is equal to zero, it means that the heat lost by the metal is equal to the heat gained by the water.

Let's plug in the known values and solve for the specific heat of the metal:

Let's assume the mass of the metal is represented by "m_metal", the specific heat of the metal is represented by "c_metal", the initial temperature of the metal is represented by "Tinitial_metal", the final temperature of the metal is represented by "Tfinal_metal", the mass of the water is represented by "m_water", the specific heat of the water is represented by "c_water", the initial temperature of the water is represented by "Tinitial_water", and the final temperature of the water is represented by "Tfinal_water".

The equation becomes:

[m_metal x c_metal x (Tfinal_metal - Tinitial_metal)] + [m_water x c_water x (Tfinal_water - Tinitial_water)] = 0

To solve for the specific heat of the metal, we rearrange the equation to isolate c_metal:

m_metal x c_metal x (Tfinal_metal - Tinitial_metal) = - m_water x c_water x (Tfinal_water - Tinitial_water)

Divide both sides of the equation by (m_metal x (Tfinal_metal - Tinitial_metal)):

c_metal = (-m_water x c_water x (Tfinal_water - Tinitial_water)) / (m_metal x (Tfinal_metal - Tinitial_metal))

By plugging in the known values for mass, specific heat, and temperature, you can calculate the specific heat of the metal using this formula.