101. Du
An insulated Cup contains 75.0 g of water
at 24.00 C. A 26.00 Sample of metal at
82.
25oC is added. The finas temperture of the
water and metal is 28.
34 C. What is the
specific heat of the metal?

Explanation:

When the sample of hot metal is placed inside the water, the metal gives off heat to the water: the temperature of the metal decreases while the temperature of the water increases, until the two reach an equilibrium temperature.

The heat given off by the metal is equal (in magnitude) to the heat absorbed by the water, so we can write:

where:

is the mass of the metal

is the specific heat of the metal

is the initial temperature of the metal

is the equilibrium temperature

is the mass of the water

is the specific heat of water

is the initial temperature of the water

And solving for , we find the specific heat of the metal:

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