A volume of 100ml of h20 is initially at room temperature (22.0c). A chilled steel rod at 2.00C is placed in the water. If the final temperature of the system is 21.2C , what is the mass of the steel bar?
To find the mass of the steel bar, we need to use the principle of energy conservation. The heat lost by the steel rod must be equal to the heat gained by the water. The formula for heat transfer is:
Q = m * c * ΔT
Where:
Q is the heat transfer
m is the mass
c is the specific heat capacity
ΔT is the change in temperature
First, we need to calculate the heat transfer for both the steel rod and the water. Let's calculate the heat lost by the steel rod:
Q_rod = m_rod * c_rod * ΔT_rod
Where:
Q_rod is the heat transfer for the steel rod
m_rod is the mass of the steel rod (unknown)
c_rod is the specific heat capacity of steel (approximately 0.45 J/g·°C)
ΔT_rod is the change in temperature of the steel rod (22.0°C - 2.0°C)
Next, let's calculate the heat gained by the water:
Q_water = m_water * c_water * ΔT_water
Where:
Q_water is the heat transfer for the water
m_water is the mass of the water (known, 100 g since the density of water is approximately 1 g/mL)
c_water is the specific heat capacity of water (approximately 4.18 J/g·°C)
ΔT_water is the change in temperature of the water (21.2°C - 22.0°C)
Since the heat lost by the steel rod is equal to the heat gained by the water, we can set up the equation as:
Q_rod = Q_water
m_rod * c_rod * ΔT_rod = m_water * c_water * ΔT_water
Now we can solve for the mass of the steel rod (m_rod):
m_rod = (m_water * c_water * ΔT_water) / (c_rod * ΔT_rod)
Substituting the known values:
m_rod = (100 g * 4.18 J/g·°C * (21.2°C - 22.0°C)) / (0.45 J/g·°C * (22.0°C - 2.0°C))
Simplifying the equation:
m_rod = (100 g * 4.18 J/g·°C * (-0.8°C)) / (0.45 J/g·°C * 20.0°C)
m_rod = -33.6 g / 9 g
m_rod ≈ -3.73 g
The negative sign indicates an error in the calculation since the mass cannot be negative. Double-check the calculations to ensure accuracy.
heat lost by steel rod + heat gained by H2O = 0
[mass rod x specific heat rod x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for the only unknown.