A 22.0 g piece of alloy at 264.8°C is dropped into a simple calorimeter that contains 175.0 g of water. The temperature of the calorimeter water increased from 20.4°C to 23.1°C.
Calculate the specific heat capacity of the alloy.
To calculate the specific heat capacity of the alloy, we need to use the equation:
Q = mcΔT
Where:
- Q is the heat transferred
- m is the mass of the substance
- c is the specific heat capacity of the substance
- ΔT is the change in temperature
First, let's calculate the heat transferred to the water using the equation:
Q_water = mcΔT
m_water = 175.0 g (mass of water)
c_water = 4.18 J/g°C (specific heat capacity of water)
ΔT_water = 23.1°C - 20.4°C = 2.7°C
Q_water = (175.0 g)(4.18 J/g°C)(2.7°C) = 2,453.35 J
Next, let's calculate the heat transferred from the alloy using the equation:
Q_alloy = mcΔT
m_alloy = 22.0 g (mass of alloy)
c_alloy = ? (specific heat capacity of the alloy)
ΔT_alloy = final temperature - initial temperature = 23.1°C - 264.8°C = -241.7°C
Note that the ΔT value for the alloy is negative because its temperature decreases.
Now we can calculate the specific heat capacity of the alloy:
Q_alloy = mcΔT
2,453.35 J = (22.0 g)(c_alloy)(-241.7°C)
Solving for c_alloy:
c_alloy = 2,453.35 J / [(22.0 g)(-241.7°C)]
c_alloy = -0.554 J/g°C
The specific heat capacity of the alloy is -0.554 J/g°C.