A 23.0-g sample of an unknown metal is heated to 91.5°C and is placed in a perfectly insulated container along with 102.g of water at an initial temperature of 21.80°C. After a short time the temperature of both the metal and water become equal at 23.80°C.
The specific Heat Capacity of water is 4.18 J/g/K in this temperature range.
What is the specific heat capacity of the metal?
heat lost by metal + heat gained by water = 0
[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0
Substitute and solve for specific heat metal.
To find the specific heat capacity of the metal, we can use the principle of heat transfer by considering the heat gained or lost by each substance involved.
First, let's determine the heat gained by the water. We can use the formula:
q = m × c × ΔT
Where:
q = heat gained/lost
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
Using the given values:
m = 102.0 g
c = 4.18 J/g/K
ΔT = 23.8°C - 21.8°C = 2.0°C
Substituting these values into the formula, we have:
q_water = (102.0 g) × (4.18 J/g/K) × (2.0 K)
Calculating this expression, we find that the heat gained by the water is:
q_water = 856.56 J
Next, let's consider the heat lost by the metal. Since the metal and water reach the same final temperature, the heat lost by the metal is equal to the heat gained by the water:
q_metal = -q_water = -856.56 J (negative sign indicates heat lost)
Now, let's determine the mass of the metal. We know that the total mass of the metal and water is 23.0 g + 102.0 g = 125.0 g. Thus, the mass of the metal can be found by subtracting the mass of water from the total mass:
m_metal = total mass - mass of water
m_metal = 125.0 g - 102.0 g
m_metal = 23.0 g
Finally, we can determine the specific heat capacity of the metal using the formula:
c_metal = q_metal / (m_metal × ΔT)
Substituting the known values:
c_metal = (-856.56 J) / (23.0 g × 2.0 K)
Calculating this expression, we find that the specific heat capacity of the metal is approximately:
c_metal = -18.7 J/g/K
The negative sign indicates that the metal lost heat during the process.