To solve this problem, we can use the principle of heat transfer. The heat lost by the silver cube and gold cube when they are placed in water is equal to the heat gained by the water. We can use the equation:
Q lost by cubes = Q gained by water
The heat lost by the silver cube can be calculated using the formula:
Q lost = (mass of silver cube) x (specific heat of silver) x (change in temperature)
The mass of the silver cube can be calculated using its density and the equation:
mass of silver cube = (density of silver) x (volume of silver cube)
The heat lost by the gold cube can be calculated using the formula:
Q lost = (mass of gold cube) x (specific heat of gold) x (change in temperature)
The mass of the gold cube can be calculated using its density and the equation:
mass of gold cube = (density of gold) x (volume of gold cube)
The change in temperature for both cubes is the final temperature of the cubes minus the initial temperature of the water:
change in temperature = (final temperature of cubes) - (initial temperature of water)
The heat gained by the water can be calculated using its specific heat, mass, and the same change in temperature:
Q gained = (mass of water) x (specific heat of water) x (change in temperature)
Since the heat lost by the cubes is equal to the heat gained by the water, we can set up the equation:
(mass of silver cube) x (specific heat of silver) x (change in temperature) + (mass of gold cube) x (specific heat of gold) x (change in temperature) = (mass of water) x (specific heat of water) x (change in temperature)
We can solve for the change in temperature using this equation:
(change in temperature) = ((mass of silver cube) x (specific heat of silver) + (mass of gold cube) x (specific heat of gold)) / ((mass of water) x (specific heat of water))
Now we can plug in the given values:
(change in temperature) = ((density of silver) x (volume of silver cube) x (specific heat of silver) + (density of gold) x (volume of gold cube) x (specific heat of gold)) / ((density of water) x (volume of water) x (specific heat of water))
Substituting the values from the table:
(change in temperature) = ((10.5 g/cm3) x (2.39 cm)3 x (0.2386 J/g·°C) + (19.3 g/cm3) x (2.73 cm)3 x (0.1256 J/g·°C)) / ((1.00 g/cm3) x (113.0 mL) x (4.184 J/g·°C))
After evaluating this expression, we can add the result to the initial temperature of the water to get the final temperature of the water when thermal equilibrium is reached.
Substance Specific heat (J/g·°C) Density (g/cm3)
gold 0.1256 19.3
silver 0.2386 10.5
water 4.184 1.00
A silver cube with an edge length of 2.39 cm and a gold cube with an edge length of 2.73 cm are both heated to 86.9 ∘C and placed in 113.0 mL of water at 19.6 ∘C . What is the final temperature of the water when thermal equilibrium is reached?
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