Final answer:
To find the specific heat capacity of a metal, the heat lost by the metal equals the heat gained by the water it's placed in. We use the formula Q=mcΔT and set the heat lost and gained equal to each other to solve for the metal's specific heat capacity.
Step-by-step explanation:
To determine the specific heat capacity of the metal in the given scenario, where 34.5 grams of hot metal at 75°C is placed in 64.0 grams of water at 25°C and they reach thermal equilibrium at 39°C, we use the principle of conservation of energy. The heat lost by the metal will equal the heat gained by the water.
The formula for the heat change is:
Q = mcΔT
where
- Q is the heat absorbed or released,
- m is the mass of the substance,
- c is the specific heat capacity,
- ΔT is the change in temperature.
For the water, we have:
Qwater = (64.0 g)(4.18 J/g°C)(39°C - 25°C)
For the metal, assuming its specific heat is 'c':
Qmetal = (34.5 g)(c)(39°C - 75°C)
Since Qmetal equals -Qwater (heat lost by metal is equal to heat gained by water), we can set them equal and solve for 'c':
(34.5 g)(c)(-36°C) = -(64.0 g)(4.18 J/g°C)(14°C)
Now, solve for 'c' to find the specific heat capacity of the metal.