A 30.5 g sample of an alloy at 94.0°C is placed into 48.7 g water at 20.3°C in an insulated coffee cup. The heat capacity of the coffee cup (without the water) is 9.2 J/K. If the final temperature of the system is 31.1°C, what is the specific heat capacity of the alloy? (c of water is 4.184 J/g×K)
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.0584 J/K
To find the specific heat capacity of the alloy, we can use the principle of conservation of energy. The heat gained by the water will be equal to the heat lost by the alloy.
First, let's calculate the heat gained by the water:
q_water = mass_water * specific_heat_water * ΔT_water
where:
- mass_water is the mass of water (48.7 g),
- specific_heat_water is the specific heat capacity of water (4.184 J/g×K),
- ΔT_water is the change in temperature of the water (final temperature - initial temperature).
ΔT_water = (31.1°C - 20.3°C) = 10.8°C
Substituting the values:
q_water = 48.7 g * 4.184 J/g×K * 10.8°C = 2229.0656 J
Now, let's calculate the heat lost by the alloy:
q_alloy = specific_heat_alloy * mass_alloy * ΔT_alloy
where:
- specific_heat_alloy is the specific heat capacity of the alloy (what we want to find),
- mass_alloy is the mass of the alloy (30.5 g),
- ΔT_alloy is the change in temperature of the alloy (final temperature - initial temperature).
ΔT_alloy = (31.1°C - 94.0°C) = -62.9°C
Substituting the values and rearranging the equation to solve for specific_heat_alloy:
q_alloy = -q_water
specific_heat_alloy * 30.5 g * -62.9°C = -2229.0656 J
specific_heat_alloy = -2229.0656 J / (30.5 g * -62.9°C)
specific_heat_alloy = 1.381 J/g×K
Therefore, the specific heat capacity of the alloy is 1.381 J/g×K.