A chunk of metal with a mass of 81.1 grams and a specific heat of 153 joules per kilogram·kelvin is heated to 95.7 degrees Celsius and placed in 144 milliliters of water at 19.5 degrees Celsius. What are the final temperatures of the metal and the water?

To find the final temperatures of the metal and water, we can use the principle of conservation of energy. The heat gained by the metal is equal to the heat lost by the water. Mathematically, this can be expressed as:

(metal mass) x (specific heat of the metal) x (change in metal temperature) = (water mass) x (specific heat of water) x (change in water temperature)

Let's calculate the initial temperature of the metal and water before they exchange heat.

The metal is initially at 95.7 degrees Celsius, while the water is at 19.5 degrees Celsius.

Now, let's convert the given quantities into suitable units. Since the specific heat of the metal is given in joules per kilogram·kelvin, we need to convert the mass of the metal from grams to kilograms. Likewise, we need to convert the volume of water from milliliters to kilograms.

Mass of metal = 81.1 grams = 0.0811 kilograms
Mass of water = 144 milliliters = 0.144 kilograms

Now, we can substitute the values into the equation:

(0.0811 kg) x (153 J/kg·K) x (final metal temperature - 95.7°C) = (0.144 kg) x (4,186 J/kg·K) x (final water temperature - 19.5°C)

Simplifying the equation further gives:

12.4203 x (final metal temperature - 95.7) = 604.704 x (final water temperature - 19.5)

Now, rearrange the equation to solve for the final metal temperature:

(final metal temperature - 95.7) = (604.704 / 12.4203) x (final water temperature - 19.5)

Finally, you can substitute the values of the given temperatures and then solve for the final metal temperature. Repeat the same process to solve for the final water temperature by rearranging the equation.