A piece of unknown metal with mass 68.6 g is heated to an initial temperature of 100 °C and dropped into 84 g of water (with an initial temperature of 20 °C) in a calorimeter. The final temperature of the system is 52.1°C. The specific heat of water is 4.184 J/g*⁰C. What is the specific heat of the metal?
To find the specific heat of the metal, we can use the principle of conservation of energy. The heat lost by the metal (Qlost) is equal to the heat gained by the water (Qgained). Both Qlost and Qgained can be calculated using the equation:
Q = m * C * ΔT
where Q is the heat energy, m is the mass, C is the specific heat, and ΔT is the change in temperature.
1. Calculate the heat lost by the metal (Qlost):
Qlost = mmetal * Cmetal * ΔTmetal
Given:
mass of metal (mmetal) = 68.6 g
initial temperature of the metal (Tinitial,metal) = 100 °C
final temperature of the system (Tfinal,system) = 52.1 °C
ΔTmetal = Tinitial,metal - Tfinal,system
2. Calculate the heat gained by the water (Qgained):
Qgained = mwater * Cwater * ΔTwater
Given:
mass of water (mwater) = 84 g
initial temperature of the water (Tinitial,water) = 20 °C
final temperature of the system (Tfinal,system) = 52.1 °C
ΔTwater = Tfinal,system - Tinitial,water
3. Set the two heat equal to each other:
Qlost = Qgained
mmetal * Cmetal * ΔTmetal = mwater * Cwater * ΔTwater
4. Solve for the specific heat of the metal (Cmetal):
Cmetal = (mwater * Cwater * ΔTwater) / (mmetal * ΔTmetal)
Substituting the given values into the equation, we can now calculate the specific heat of the metal.
what is the answer??????????????????????
what is the answer !?!?!?!?
heat gained by water = heat lost by metal
amount of heat = mass * specific heat * temperature change