determine the final temp when 45.8 g of aluminum at -5.2 degrees C is added to a mixture of 45.0 grams of ice at 0.00 degrees C and 2000.0 g of water at 95.0 degrees C.
First, assume the final temp will be between 0 and 95. If this is not the case, you will get an odd answer.
The sum of all the heats gained will be zero (some will be negative, heat lost).
Heat gained by Al+ heatmeltingice+heat heating ice water + heat from hot water=0
45.8*Calum*(Tf-(-5.2))+45*Hfice+45*cwater(Tf-0)+2000*cwater*(Tf-95)=0
solve for Tf
To determine the final temperature when substances of different temperatures are mixed together, you can use the principle of conservation of energy. The energy gained or lost by each substance can be calculated using the equation:
q = m * c * ΔT
where:
- q is the energy gained or lost
- m is the mass of the substance
- c is the specific heat capacity of the substance
- ΔT is the change in temperature
Step 1: Calculate the energy gained or lost by the aluminum:
q_aluminum = m_aluminum * c_aluminum * ΔT_aluminum
Given:
m_aluminum = 45.8 g
c_aluminum = 0.897 J/g°C (specific heat capacity of aluminum)
ΔT_aluminum = final temperature - initial temperature
Since the initial temperature of the aluminum is -5.2 degrees C and we want to find the final temperature, we can rewrite the equation as:
q_aluminum = 45.8 g * 0.897 J/g°C * (final temperature - (-5.2°C))
Step 2: Calculate the energy gained or lost by the ice:
q_ice = m_ice * c_ice * ΔT_ice
Given:
m_ice = 45.0 g
c_ice = 2.09 J/g°C (specific heat capacity of ice)
ΔT_ice = final temperature - initial temperature
In this case, the initial temperature of the ice is 0.00 degrees C. Rewrite the equation as:
q_ice = 45.0 g * 2.09 J/g°C * (final temperature - 0.00°C)
Step 3: Calculate the energy gained or lost by the water:
q_water = m_water * c_water * ΔT_water
Given:
m_water = 2000.0 g
c_water = 4.18 J/g°C (specific heat capacity of water)
ΔT_water = final temperature - initial temperature
Here, the initial temperature of the water is 95.0 degrees C. Rewrite the equation as:
q_water = 2000.0 g * 4.18 J/g°C * (final temperature - 95.0°C)
Step 4: Set up the conservation of energy equation:
The total energy gained or lost must be equal to zero, assuming no energy is lost to the surroundings.
q_aluminum + q_ice + q_water = 0
Plug in the calculated values and the three equations into the conservation of energy equation and solve for the final temperature.
Note: It's important to always convert temperatures to Kelvin before plugging them into the equations because the specific heat capacities are given in joules per gram per degree Celsius.
Given all the information, you can now solve for the final temperature by summing up the individual energy changes and solving the equation.