A 55 grams copper calorimeter contains an unknown mass of water at 18 degrees celcius. When 755 grams of alloy at 100 degrees celcius is dropped into the calorimeter ,the resulting temperature is 20.4 degrees celcius. Determine the mass of water.
To determine the mass of water in the calorimeter, we can use the formula for heat transfer:
Q = mcΔT
Where:
Q = heat transferred (in joules)
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
First, let's calculate the heat transferred from the alloy to the water in the calorimeter. Since it is isolated, the heat gained by the water is equal to the heat lost by the alloy.
Q_water = Q_alloy
Since both the water and the alloy have their own specific heat capacities, we can write the equation as:
m_water * c_water * ΔT_water = m_alloy * c_alloy * ΔT_alloy
Given:
c_water = 4.18 J/g°C (specific heat capacity of water)
c_alloy = unknown (specific heat capacity of the alloy)
m_alloy = 755 g (mass of the alloy)
ΔT_water = 20.4°C - 18°C = 2.4°C
ΔT_alloy = 20.4°C - 100°C = -79.6°C (negative sign because it lost heat)
Substituting the given values into the equation:
m_water * 4.18 J/g°C * 2.4°C = 755 g * c_alloy * (-79.6°C)
Now, let's solve for the mass of water (m_water):
m_water = (755 g * c_alloy * -79.6°C) / (4.18 J/g°C * 2.4°C)
We still need to determine the specific heat capacity of the alloy (c_alloy) to calculate the mass of water. Unfortunately, this information is missing from the question. Without knowing the specific heat capacity of the alloy, we cannot calculate the mass of water. You would need to provide that information in order to find the answer.