what will be the final temperature when equal amounts of ice at-10 degree is added to water at 60 degree c
To determine the final temperature when ice at -10 degrees Celsius is added to water at 60 degrees Celsius, you can use the principle of energy conservation.
First, we need to calculate the amount of energy gained or lost by both the ice and the water during the process. We will assume that the ice is initially at its melting point (-10 degrees Celsius) and that no energy is lost to the surroundings.
The energy gained or lost by an object can be calculated using the formula:
Q = m * c * ΔT
Where:
Q is the energy gained or lost
m is the mass of the object
c is the specific heat capacity of the substance
ΔT is the change in temperature
For ice turning into water:
Q_ice = m_ice * cice * ΔT_ice
For water:
Q_water = m_water * cwater * ΔT_water
Since we are adding equal masses of ice and water, m_ice = m_water = m
The final temperature of the system will be the temperature at which the energy gained by the ice is equal to the energy lost by the water.
Q_ice = -Q_water (Note the negative sign indicates energy loss)
m * cice * ΔT_ice = -m * cwater * ΔT_water
Simplifying the equation, dividing both sides by m, we get:
cice * ΔT_ice = -cwater * ΔT_water
Now we plug in the values:
cice = specific heat capacity of ice = 2.09 J/g°C
cwater = specific heat capacity of water = 4.18 J/g°C
ΔT_ice = final temperature of ice - initial temperature of ice = 0 - (-10) = 10°C
ΔT_water = final temperature of water - initial temperature of water = final temperature of water - 60°C
Substituting the values into the equation:
2.09 * 10 = -4.18 * ΔT_water
Simplifying it further:
20.9 = -4.18 * ΔT_water
Dividing both sides by -4.18:
ΔT_water = -20.9 / 4.18 ≈ -5°C
The negative sign indicates that the water will cool down.
Now, to find the final temperature, we subtract the change in temperature from the initial temperature of the water:
Final temperature = 60 - 5 = 55 degrees Celsius.
Therefore, the final temperature of the system will be approximately 55 degrees Celsius.