A cube of ice is taken from the freezer at -9.5 degree Celsius and placed in a 99 g aluminum calorimeter filled with 327 g of water at room temperature of 20.0 degree celsius. The final situation is observed to be all water at 17.0 degree Celsius.
What was the mass of the ice cube?
A laser used to weld detached retinas emits light with a wavelength of 652 in pulses that are 20.0 in duration. The average power expended during each pulse is 0.600 .
To find the mass of the ice cube, we can use the principle of conservation of energy. The energy lost by the ice cube when it melts is equal to the energy gained by the water and the aluminum calorimeter. We can use the specific heat capacities of water and aluminum to calculate this energy transfer.
The energy transferred from the ice cube to the water can be calculated using the equation:
Q = m * c * ΔT
Where:
Q is the energy transferred
m is the mass
c is the specific heat capacity
ΔT is the change in temperature
The ice cube starts at -9.5°C and melts to 0°C, so the change in temperature is 0 - (-9.5) = 9.5°C.
The energy transferred from the ice cube to the water is therefore:
Q1 = m1 * c1 * ΔT1
Where:
m1 is the mass of the ice cube (what we want to find)
c1 is the specific heat capacity of ice (2.09 J/g°C, also known as the heat of fusion)
ΔT1 is the change in temperature (9.5°C)
Next, we can determine the energy transferred from the water to the aluminum calorimeter.
The energy transferred from the water to the aluminum calorimeter is given by:
Q2 = m2 * c2 * ΔT2
Where:
m2 is the mass of the water (327 g)
c2 is the specific heat capacity of water (4.18 J/g°C)
ΔT2 is the change in temperature of the water (17°C - 20°C = -3°C)
Since the system is isolated, the energy transferred from the ice cube to the water is equal to the energy transferred from the water to the aluminum calorimeter:
Q1 = Q2
m1 * c1 * ΔT1 = m2 * c2 * ΔT2
Plugging in the known values:
m1 * 2.09 J/g°C * 9.5°C = 327 g * 4.18 J/g°C * (-3°C)
Simplifying the equation:
m1 = (327 g * 4.18 J/g°C * (-3°C)) / (2.09 J/g°C * 9.5°C)
m1 = 27.84 g
Therefore, the mass of the ice cube is approximately 27.84 grams.