Temprature of mixture
63.85g piece metall with specific heat capacity of 0,078cal /gK at 89.9 C is dropped into calorimeter with 52.8 ml water solution at 18,4 C
specific heat capacity of water solution is 1,131kcal/lK
finel eqibilirium temrature of the mixture
I assume the density of the solution is 1.0 g/mL which probably is not right. Since the specific heat of the solution is 1.113 cal/g*C which is a deviation from the normal of 1 cal/g*K, I would expect the density to be greater than 1. If your problem gives the density and it is greater than 1.0, then use mass H2O = volume of water x density of water instead of the 52.8 I've used below.
[mass metal x specific heat metal x (Tfinal - Tinitial)] + [mass H2O x specific heat H2O x (Tfinal - Tinitial)] = 0
[63.85 g x 0.078 cal/g*K x (Tfinal - 89.9)] + [ 52.8 g x 1.113 cal/g*C x (Tfinal - 18.4)] = 0
Solve for Tfinal which is the only unknown in the above.
To find the final equilibrium temperature of the mixture, we can use the principle of conservation of energy.
The heat gained by the metal piece will be equal to the heat lost by the water solution in the calorimeter.
First, let's calculate the heat gained by the metal piece using the specific heat capacity of the metal:
q_gain_metal = mass_metal * specific_heat_metal * (final_temp - initial_temp_metal)
Given:
mass_metal = 63.85 g
specific_heat_metal = 0.078 cal/gK
initial_temp_metal = 89.9°C
Let's assume the final equilibrium temperature of the mixture is "T".
So, the heat gained by the metal piece can be calculated as:
q_gain_metal = 63.85 g * 0.078 cal/gK * (T - 89.9)
Now, let's calculate the heat lost by the water solution using the specific heat capacity of the solution:
q_loss_water = mass_water * specific_heat_water * (final_temp - initial_temp_water)
Given:
mass_water = 52.8 ml
specific_heat_water = 1.131 kcal/lK
initial_temp_water = 18.4°C
Since the mass of water is given in ml, we need to convert it to grams using the density of water:
1 ml of water = 1 g
So, mass_water = 52.8 g
Using these values, the heat lost by the water solution can be calculated as:
q_loss_water = 52.8 g * 1.131 kcal/lK * (T - 18.4)
Since q_gain_metal = q_loss_water (as per the principle of conservation of energy):
63.85 g * 0.078 cal/gK * (T - 89.9) = 52.8 g * 1.131 kcal/lK * (T - 18.4)
Now, we can solve this equation to find the final equilibrium temperature "T" of the mixture.