106 g of iron at 84.0°C are placed in contact with 205 g of silver at 11.0°C. If no heat is lost to the surroundings, what is the final temperature of the metals? The specific heat of iron is 0.418 J/g·°C and that of silver is 0.251 J/g·°C.
92.0 g of a metal at 92.0°C are added to 53.0 g of water at 30.6°C. When the system reaches constant temperature, the temperature is 38.7°C. What is the specific heat of the metal? The specific heat of water is 4.184 J/g·°C.
heat lost by Fe + heat gained by Ag = 0
[mass Fe x specific heat Fe x (Tfinal-Tintial)] + [mass Ag x specific heat Ag x (Tfinal-Tinitial)] = 0
Substitute and solve for Tfinal.
The second problem is worked the same way.
To solve these problems, we can use the principle of conservation of energy, which states that the heat lost by one object is equal to the heat gained by another object.
For the first problem, let's denote the final temperature as "Tf".
The heat lost by the iron can be calculated using the formula:
Qlost = mass_iron * specific_heat_iron * (initial_temperature_iron - Tf)
The heat gained by the silver can be calculated using the formula:
Qgained = mass_silver * specific_heat_silver * (Tf - initial_temperature_silver)
Since no heat is lost to the surroundings, we can set Qlost equal to Qgained:
mass_iron * specific_heat_iron * (initial_temperature_iron - Tf) = mass_silver * specific_heat_silver * (Tf - initial_temperature_silver)
Substituting the given values, we have:
106g * 0.418 J/g·°C * (84.0°C - Tf) = 205g * 0.251 J/g·°C * (Tf - 11.0°C)
Now, we can solve this equation to find the final temperature Tf.
For the second problem, we can use the same principle of conservation of energy.
The heat lost by the metal can be calculated using the formula:
Qlost = mass_metal * specific_heat_metal * (initial_temperature_metal - Tf)
The heat gained by the water can be calculated using the formula:
Qgained = mass_water * specific_heat_water * (Tf - initial_temperature_water)
Again, since no heat is lost to the surroundings, we can set Qlost equal to Qgained:
mass_metal * specific_heat_metal * (initial_temperature_metal - Tf) = mass_water * specific_heat_water * (Tf - initial_temperature_water)
Substituting the given values, we have:
92.0g * specific_heat_metal * (92.0°C - 38.7°C) = 53.0g * 4.184 J/g·°C * (38.7°C - 30.6°C)
Now, we can solve this equation to find the specific heat of the metal.