A piece of metal weighing 5.10g at a temperature of 48.6 degree Celsius was placed in a calorimeter in 20.00 mL of water at 22.1 degree Celsius. The final equilibrium temperature was found to be 29.2 degree celsius. What is the specific heat of the metal?
I assume we are to ignore the calorimeter constant.
[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x secific heat H2O x (Tfinal-Tinitial)] = 0.
Substitute and solve for s.h. metal.
To find the specific heat of the metal, use the principle of energy conservation:
1. First, calculate the heat gained by the water using the formula:
Q_water = m_water * c_water * ΔT_water,
where:
Q_water is the heat gained by the water,
m_water is the mass of water,
c_water is the specific heat capacity of water (4.18 J/g°C),
ΔT_water is the change in temperature of water.
Given:
m_water = 20.00 g
c_water = 4.18 J/g°C
ΔT_water = (final temperature of water) - (initial temperature of water)
= 29.2°C - 22.1°C
2. Next, calculate the heat lost by the metal using the formula:
Q_metal = m_metal * c_metal * ΔT_metal,
where:
Q_metal is the heat lost by the metal,
m_metal is the mass of the metal,
c_metal is the specific heat capacity of the metal,
ΔT_metal is the change in temperature of the metal.
Given:
m_metal = 5.10 g
ΔT_metal = (final temperature of metal) - (initial temperature of metal)
= 29.2°C - 48.6°C
3. Since the system is in thermal equilibrium, the heat lost by the metal is gained by the water. Therefore:
Q_water = Q_metal
4. Substitute the values into the equation from step 1 and step 2, and set them equal to find the specific heat capacity of the metal:
m_water * c_water * ΔT_water = m_metal * c_metal * ΔT_metal
Solve for c_metal:
c_metal = (m_water * c_water * ΔT_water) / (m_metal * ΔT_metal)
5. Substitute the given values and solve for c_metal:
c_metal = (20.00 g * 4.18 J/g°C * (29.2°C - 22.1°C)) / (5.10 g * (29.2°C - 48.6°C))
Therefore, the specific heat of the metal is calculated to be:
c_metal = -30.98 J/g°C
To determine the specific heat of the metal, we can use the principle of heat transfer. The heat gained by the metal would be equal to the heat lost by the water in the calorimeter.
First, let's calculate the heat gained by the metal.
The heat gained by the metal can be calculated using the formula:
Q_metal = (mass_metal) x (specific_heat_metal) x (change_in_temperature)
Given:
mass_metal = 5.10 g
change_in_temperature = (final temperature - initial temperature) = (29.2 - 48.6) = -19.4 °C
Q_metal = ?
We need to find the specific heat of the metal, so let's solve for it.
Q_metal = (5.10 g) x (specific_heat_metal) x (-19.4 °C)
Now, let's calculate the heat lost by the water (calorimeter).
The heat lost by the water can be calculated using the formula:
Q_water = (mass_water) x (specific_heat_water) x (change_in_temperature)
Given:
mass_water = 20.00 g (since the density of water is roughly equivalent to 1 g/cm^3)
change_in_temperature = (final temperature - initial temperature) = (29.2 - 22.1) = 7.1 °C
Q_water = 0.999 g/mL (specific heat of water) x 20.00 mL x 7.1 °C
Now, since the heat gained by the metal must be equal to the heat lost by the water, we can equate the two equations:
(5.10 g) x (specific_heat_metal) x (-19.4 °C) = (0.999 g/mL) x (20.00 mL) x (7.1 °C)
Now, solve for specific_heat_metal:
specific_heat_metal = [(0.999 g/mL) x (20.00 mL) x (7.1 °C)] / [(5.10 g) x (-19.4 °C)]
By plugging in the values and performing the calculations, you will find the specific heat of the metal.