If 0.045 kg of ice at 0 C is added to 0.390 kg of water at 34 C in a 0.150 kg aluminum calorimeter cup, what is the final temperature of the water?
T = degree C
Write the heat balance equation, with the aluminum cup starting out at the same temperature as the water (34 C). You will need to determine if all of the ice melts or not. Solve for final T. It would be 0 C is not all of the ice melts.
Show your work for futher assistance, if needed.
To find the final temperature of the water, we can use the principle of conservation of energy.
Let's break down the problem into a few steps:
Step 1: Find the heat gained by the ice (Q_ice).
The heat gained by the ice can be calculated using the formula:
Q_ice = mass_ice * specific_heat_ice * temperature_change_ice
Given:
mass_ice = 0.045 kg
specific_heat_ice = 2090 J/kg°C (specific heat capacity of ice)
temperature_change_ice = final temperature - initial temperature = T - 0°C = T°C
Step 2: Find the heat lost by the water (Q_water).
The heat lost by the water can be calculated using the formula:
Q_water = mass_water * specific_heat_water * temperature_change_water
Given:
mass_water = 0.390 kg
specific_heat_water = 4186 J/kg°C (specific heat capacity of water)
temperature_change_water = final temperature - initial temperature = T - 34°C = (T - 34)°C
Step 3: Find the heat gained by the aluminum calorimeter cup (Q_cup).
The heat gained by the cup can be calculated using the formula:
Q_cup = mass_cup * specific_heat_cup * temperature_change_cup
Given:
mass_cup = 0.150 kg
specific_heat_cup = 900 J/kg°C (specific heat capacity of aluminum)
temperature_change_cup = final temperature - initial temperature = T - 0°C = T°C
Step 4: Apply the principle of conservation of energy.
According to the principle of conservation of energy, the heat gained by the ice must be equal to the sum of the heat lost by the water and the heat gained by the cup:
Q_ice = Q_water + Q_cup
Step 5: Solve for the final temperature (T).
By rearranging the equation from step 4, we can solve for the final temperature (T):
Q_ice - Q_water - Q_cup = 0
mass_ice * specific_heat_ice * temperature_change_ice - mass_water * specific_heat_water * temperature_change_water - mass_cup * specific_heat_cup * temperature_change_cup = 0
Now, we can substitute the given values and solve for the final temperature (T).
Note: Remember to convert the final temperature (T) into degrees Celsius by subtracting 273.15 (if necessary) since we'll be using SI units in the calculations.