a 425 g cylinder of brass is heated to 90/0 degree C and placed in a calorimeter containing 334 g of water at 25.0 degree C. The water is tirred and its highest temperature is recorded as 32.0 degree C. From the thermal energy gained by the water, determine the specific heat of brass. The specific heat of water is 4.18 J/g degree C.
To determine the specific heat of brass, we need to apply the principle of conservation of energy. The amount of thermal energy gained by the water is equal to the amount of thermal energy lost by the brass cylinder.
1. Calculate the thermal energy gained by the water:
Q_water = mass_water * specific_heat_water * ΔT_water
Q_water = 334 g * 4.18 J/g°C * (32.0°C - 25.0°C)
2. Calculate the thermal energy lost by the brass cylinder:
Q_brass = mass_brass * specific_heat_brass * ΔT_brass
Q_brass = 425 g * specific_heat_brass * (32.0°C - 90.0°C)
Since the thermal energy gained and lost are equal, we can set up an equation:
Q_water = Q_brass
334 g * 4.18 J/g°C * (32.0°C - 25.0°C) = 425 g * specific_heat_brass * (32.0°C - 90.0°C)
Now we can solve for the specific heat of brass.
specific_heat_brass = (334 g * 4.18 J/g°C * (32.0°C - 25.0°C)) / (425 g * (32.0°C - 90.0°C))
Calculating the specific heat of brass using the given values:
specific_heat_brass = (1394.36 J) / (425 g * (-58.0°C))
specific_heat_brass = (1394.36 J) / (-24,850 g°C)
specific_heat_brass ≈ -0.056 J/g°C
Therefore, the specific heat of brass is approximately -0.056 J/g°C. Note that there is a negative sign due to the fact that the brass is losing thermal energy.