Question

A 170.0-g sample of metal at 73.00°C is added to 170.0 g of H₂O(l) at 26.00°C in an insulated container. The temperature rises to 27.70°C. Neglecting the heat capacity of the container, what is the specific heat capacity of the metal?

Answer 1

To determine the specific heat capacity of the metal, we apply the law of conservation of energy. By setting up an equation where the heat lost by the metal equals the heat gained by the water, and substituting the known values and solving for the specific heat, we can find the specific heat capacity of the metal.

Step-by-step explanation:

To calculate the specific heat capacity of the metal, we use the principle of conservation of energy, which states that the heat lost by the metal will be equal to the heat gained by the water:

qmetal = -qwater

Given that the specific heat capacity of water is 4.18 J/g°C, and the mass and temperature changes of the metal and water are known, we can express this as:

(mass of metal)(specific heat of metal)(change in temp of metal) = - (mass of water)(specific heat of water)(change in temp of water)

Plugging in the values:

(170.0 g)(cmetal)(27.70°C - 73.00°C) = -(170.0 g)(4.18 J/g°C)(27.70°C - 26.00°C)

By solving for cmetal, we can find the specific heat capacity of the metal. The negative sign indicates that the direction of heat flow is opposite for the metal and the water.