A 0.300 kg iron horseshoe that is initially at 550°C is dropped into a bucket containing 19.4 kg of water at 21.1°C. What is the final equilibrium temperature (in °C)? Neglect any heat transfer to or from the surroundings. Do not enter units.
To find the final equilibrium temperature, we can apply the principle of conservation of energy. The heat lost by the hot object (horseshoe) will be equal to the heat gained by the cold object (water).
The heat gained or lost by an object can be calculated using the formula:
Q = mcΔT
Where:
Q is the heat gained or lost
m is the mass of the object
c is the specific heat capacity of the material
ΔT is the change in temperature
First, let's calculate the heat lost by the hot horseshoe. The specific heat capacity of iron is 450 J/kg°C.
Q_hot = mcΔT_hot
= (0.300 kg)(450 J/kg°C)(550°C - T_f)
Next, let's calculate the heat gained by the cold water. The specific heat capacity of water is 4186 J/kg°C.
Q_cold = mcΔT_cold
= (19.4 kg)(4186 J/kg°C)(T_f - 21.1°C)
According to the principle of conservation of energy, Q_hot = Q_cold.
So, we can equate the two equations:
(0.300 kg)(450 J/kg°C)(550°C - T_f) = (19.4 kg)(4186 J/kg°C)(T_f - 21.1°C)
Now, let's solve this equation to find the final equilibrium temperature (T_f).