94.0 g of a metal at 88.0°C are added to 55.0 g of water at 26.0°C. When the system reaches constant temperature, the temperature is 39.3°C. What is the specific heat of the metal? The specific heat of water is 4.184 J/g·°C.
same procedure.
In a two system problem, the easier way is to realize that the heat lost + heat gained = 0 and solve for the only unknown in the equation.
mass1 x specific heat1 x (Tfinal-Tinitial) + mass2 x specific heat 2 x (Tfinal-Tinitial) = 0
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Good. Thank you. But I see that it's the same computer.
To find the specific heat of the metal, we can use the principle of conservation of energy. The energy lost by the metal when it cools down is equal to the energy gained by the water when it heats up.
1. Calculate the energy lost by the metal:
- Mass of the metal = 94.0 g
- Initial temperature of the metal = 88.0°C
- Final temperature of the metal = 39.3°C
The energy lost by the metal can be calculated using the formula:
Energy = mass × specific heat × temperature change
(Note: The temperature change is the final temperature minus the initial temperature)
Energy lost by the metal = 94.0 g × specific heat of the metal × (39.3°C - 88.0°C)
2. Calculate the energy gained by the water:
- Mass of the water = 55.0 g
- Initial temperature of the water = 26.0°C
- Final temperature of the water = 39.3°C
The energy gained by the water can be calculated using the same formula:
Energy = mass × specific heat × temperature change
Energy gained by the water = 55.0 g × 4.184 J/g·°C × (39.3°C - 26.0°C)
3. Set the energy lost by the metal equal to the energy gained by the water:
Energy lost by the metal = Energy gained by the water
Solve for the specific heat of the metal.
By substituting the given values in the above equation, you can solve for the specific heat of the metal.