A 24.0 g metal cube at 85.5 °C is placed into a calorimeter containing 125 mL of water at 20.0 °C. The final equilibrium temperature of the metal cube and the water in the calorimeter is 24.8 °C. Determine the specific heat of the metal
the sum of heats gained is zero.
24*cmetal*(85.5-24.8)+125*cwater*(24.8-20)=0
solver for cmetal.
To determine the specific heat of the metal, you will need to apply the principle of conservation of energy and use the formula:
q = mcΔT
Where:
- q represents the heat exchanged between the metal and the water.
- m is the mass of the water in grams.
- c is the specific heat capacity of the metal in J/g°C.
- ΔT is the change in temperature between the initial and final states.
Step 1: Calculate the heat exchanged between the metal and the water.
First, find the mass of the water in grams by converting the volume given (125 mL) to grams using the density of water, which is approximately 1 g/mL.
mass_water = volume_water x density_water
mass_water = 125 mL x 1 g/mL
mass_water = 125 g
Step 2: Determine the change in temperature.
ΔT = final temperature - initial temperature
ΔT = 24.8°C - 20.0°C
ΔT = 4.8°C
Step 3: Determine the specific heat of the metal.
Now, rearrange the equation q = mcΔT to solve for c.
c = q / (m x ΔT)
Substitute the given values into the equation:
c = q / (mass_water x ΔT)
Step 4: Calculate the heat exchanged, q.
We can use the same formula, q = mcΔT, to calculate q. Since the calorimeter and the metal are in thermal equilibrium at the final temperature, the heat gained by the water is equal to the heat lost by the metal.
q = -q
(q_water = -q_metal)
Therefore, we can calculate q_metal using:
q_metal = q_water
q_metal = (mass_water x c x ΔT)
Step 5: Substitute the known values into the equation to solve for c.
c = q_metal / (mass_water x ΔT)
c = (mass_water x c x ΔT) / (mass_water x ΔT)
c = c
Since the mass_water and ΔT terms cancel out, the specific heat of the metal (c) is equal to 1.0.
Therefore, the specific heat of the metal is 1.0 J/g°C.