Determine the resulting temperature when 1kg of ice at 0 Degree celcius is mixed with 9kg of water.

not without knowing the water temp at start

To determine the resulting temperature when ice and water are mixed, we need to consider the concept of thermal equilibrium. In this scenario, the ice will melt, and the resulting water will reach thermal equilibrium with the initial 9kg of water.

To find the resulting temperature, we can use the principle of conservation of energy, known as the heat equation:

Q = m1 * c1 * ΔT1 + m2 * c2 * ΔT2

Where:
Q represents the heat exchanged (in joules)
m1 and m2 represent the masses of the substances involved (in kilograms)
c1 and c2 represent the specific heat capacities of the substances (in joules per kilogram degree Celsius)
ΔT1 and ΔT2 represent the temperature changes (in degrees Celsius)

In this case, we have:
m1 = 1kg, the mass of ice
m2 = 9kg, the mass of water
c1 = 2.09 J/g°C, the specific heat capacity of ice
c2 = 4.18 J/g°C, the specific heat capacity of water

Now, let's calculate the heat exchanged for each substance.

For the ice:
Q1 = m1 * c1 * ΔT1
Q1 = 1kg * 2.09 J/g°C * (0°C - 0°C) = 0 Joules

Since the ice is initially at 0°C and its temperature doesn't change during melting, no heat is exchanged.

For the water:
Q2 = m2 * c2 * ΔT2
Q2 = 9kg * 4.18 J/g°C * (T - 0°C)

The heat exchanged by the water will contribute to the temperature change. Since the ice is melting, the water's temperature will rise to the final equilibrium temperature T.

As per the conservation of energy principle, the heat gained by water is equal to the heat lost by ice:

Q2 = -Q1

Substituting the values:

9kg * 4.18 J/g°C * (T - 0°C) = 0 Joules

Now, let's solve for T:

37.62 * (T - 0) = 0
T = 0°C

Thus, the resulting temperature when 1kg of ice at 0°C is mixed with 9kg of water is 0°C (the melting point of ice).