A 155 g aluminum cylinder is removed from a liquid nitrogen bath, where it has been cooled to -196 degrees c. The cylinder is immediately placed in a insulated cup containing 80g of water at 15 degrees c. What is the equilibrium temperature of this system?
heat gained by Al equals heat lost by H2O
(mass Al) * (temp change Al) * (specific heat Al) =
(mass H2O) * (temp change H2O) * (specific heat H2O)
the temperature changes are from the starting temperatures
to the equilibrium temperature
Thank you!
To determine the equilibrium temperature of the system, we can use the principle of conservation of energy.
Step 1: Calculate the heat gained by the aluminum cylinder when it warms up from -196°C to the equilibrium temperature.
The heat gained by the aluminum cylinder can be calculated using the formula:
Q1 = m1 * c1 * (Tf - Ti)
Where:
- Q1 is the heat gained by the aluminum cylinder
- m1 is the mass of the aluminum cylinder (155 g)
- c1 is the specific heat capacity of aluminum (0.897 J/g°C)
- Tf is the final temperature (equilibrium temperature)
- Ti is the initial temperature (-196°C)
Q1 = 155 g * 0.897 J/g°C * (Tf - (-196°C))
Step 2: Calculate the heat lost by the water when it cools down from 15°C to the equilibrium temperature.
The heat lost by the water can be calculated using the formula:
Q2 = m2 * c2 * (Tf - Ti)
Where:
- Q2 is the heat lost by the water
- m2 is the mass of the water (80 g)
- c2 is the specific heat capacity of water (4.184 J/g°C)
- Tf is the final temperature (equilibrium temperature)
- Ti is the initial temperature (15°C)
Q2 = 80 g * 4.184 J/g°C * (Tf - 15°C)
Step 3: Set Q1 equal to Q2 to find the equilibrium temperature.
Q1 = Q2
155 g * 0.897 J/g°C * (Tf - (-196°C)) = 80 g * 4.184 J/g°C * (Tf - 15°C)
Now, we can solve this equation to find the equilibrium temperature (Tf).
To find the equilibrium temperature of the system, we can use the principle of heat transfer, which states that heat lost by one substance is equal to the heat gained by another substance.
First, let's calculate the heat lost by the aluminum cylinder. We can use the formula:
Q = m * c * ΔT
Where:
Q is the heat lost
m is the mass of the aluminum cylinder
c is the specific heat capacity of aluminum (0.903 J/g°C)
ΔT is the change in temperature
The initial temperature of the aluminum cylinder is -196°C, and the final equilibrium temperature is unknown. So, the change in temperature (ΔT) is:
ΔT = (unknown) - (-196°C)
Next, let's calculate the heat gained by the water. We can use the same formula:
Q = m * c * ΔT
Where:
Q is the heat gained
m is the mass of the water
c is the specific heat capacity of water (4.18 J/g°C)
ΔT is the change in temperature
The initial temperature of the water is 15°C, and the final equilibrium temperature is unknown. So, the change in temperature (ΔT) is:
ΔT = (unknown) - 15°C
Since the heat lost by the aluminum cylinder is equal to the heat gained by the water (assuming no heat is lost to the surroundings), we can set these two equations equal to each other:
m1 * c1 * (unknown - (-196°C)) = m2 * c2 * (unknown - 15°C)
Substituting the given values:
m1 = 155g (mass of aluminum cylinder)
c1 = 0.903 J/g°C (specific heat capacity of aluminum)
m2 = 80g (mass of water)
c2 = 4.18 J/g°C (specific heat capacity of water)
155 * 0.903 * (unknown + 196) = 80 * 4.18 * (unknown - 15)
Now, we can solve this equation to find the equilibrium temperature of the system.