A silver block, initially at 59.4∘C^\circ C, is submerged into 100.0 g{\rm g} of water at 25.3∘C^\circ C, in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 27.6∘C^\circ C.
I don't know what I'm doing
heat lost by Ag + heat gained by water = 0
[mass Ag x specific heat Ag x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for Tf, the only unknown.
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To understand how to calculate the specific heat capacity of the silver block based on the given information, we need to apply the principle of conservation of energy.
Here are the steps to calculate the specific heat capacity of the silver block:
Step 1: Determine the heat gained by the water:
To calculate the heat gained by the water, we can use the equation:
Q_water = m_water * c_water * ΔT_water
Where:
Q_water is the heat gained by the water (in joules)
m_water is the mass of the water (in grams) = 100.0 g
c_water is the specific heat capacity of water (in joules per gram per degree Celsius) = 4.18 J/g°C
ΔT_water is the change in temperature of the water = Tf - Ti
Substituting the given values:
Q_water = 100.0 g * 4.18 J/g°C * (27.6°C - 25.3°C)
Step 2: Determine the heat lost by the silver block:
To calculate the heat lost by the silver block, we can use the equation:
Q_block = m_block * c_block * ΔT_block
Where:
Q_block is the heat lost by the silver block (in joules)
m_block is the mass of the silver block (in grams)
c_block is the specific heat capacity of the silver block (in joules per gram per degree Celsius)
ΔT_block is the change in temperature of the silver block = Tf - Ti
Since the initial and final temperatures of the silver block are not given, we can assume that the initial and final temperatures of the block are the same as the final temperature of the mixture (27.6°C).
Substituting the given values:
Q_block = m_block * c_block * (27.6°C - 27.6°C)
Step 3: Apply the principle of conservation of energy:
According to the principle of conservation of energy, the heat gained by the water is equal to the heat lost by the silver block. Therefore:
Q_water = -Q_block
Step 4: Calculate the specific heat capacity of the silver block:
Since Q_water = -Q_block, we can equate the equations from Step 1 and Step 2:
m_water * c_water * ΔT_water = -m_block * c_block * ΔT_block
Rearranging the equation, we can solve for the specific heat capacity of the silver block (c_block):
c_block = -m_water * c_water * ΔT_water / (m_block * ΔT_block)
Substituting the given values:
c_block = -100.0 g * 4.18 J/g°C * (27.6°C - 25.3°C) / (m_block * (27.6°C - 27.6°C))
Simplifying the equation:
c_block = -100.0 g * 4.18 J/g°C * (2.3°C) / 0
Since the change in temperature of the silver block is 0 (ΔT_block = 0), it means that the final temperature is the same as the initial temperature. Therefore, we cannot determine the specific heat capacity of the silver block with the given information.