Thermal Equilibrium Video Lessons

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Problem: On a hot summer day, you decide to make some iced tea. First, you brew 1.50 L of hot tea and leave it to steep until it has reached a temperature of Ttea = 75.0°C. You then add 0.975 kg of ice taken from the freezer at a temperature of Tice = 0°C. By the time the mix reaches equilibrium, all of the ice has melted. What is the final temperature Tf of the mixture? For the purpose of this problem, assume that the tea has the same thermodynamic properties as plain water.• The specific heat of water is x = 4190 J/kg•°C.• The heat of fusion of ice is Lf = 3.33×105 J/kg.• The density of the tea is ρ = 1.00 kg/L.Part A. In this process, the systems undergo which of the following changes?A. phase changes onlyB. temperature changes onlyC. both phase and temperature changesD. neither phase nor temperature changesPart B. Determine which quantities are known and which are unknown • Initial mass of tea: mtea• Initial mass of ice: mice • initial volume of tea: Vtea• Initial volume of ice: Vice• Initial temperature of tea:Ttea• Initial temperature of ice: Tice• final temperature of system: Tf

FREE Expert Solution

Use the concept of calorimetry where the ice at 0°C absorbs the heat from the tea at 75.0°C to determine the final temperature Tf of the mixture

In Calorimetry, we can setup the thermal equilibrium as:


- Q = +Q

where -Q is tea releasing the heat (hotter) to the +Q (colder) ice.


Recall that Q or heat can be calculated as:

Q = mCT

where m is mass in gC is specific heat and ΔT as the change in temperature (ΔT = Tf – Ti) in °C

In this case, we have the C for water as 4.184 J/g°C


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Problem Details

On a hot summer day, you decide to make some iced tea. First, you brew 1.50 L of hot tea and leave it to steep until it has reached a temperature of Ttea = 75.0°C. You then add 0.975 kg of ice taken from the freezer at a temperature of Tice = 0°C. By the time the mix reaches equilibrium, all of the ice has melted. What is the final temperature Tf of the mixture? 

For the purpose of this problem, assume that the tea has the same thermodynamic properties as plain water.

• The specific heat of water is x = 4190 J/kg•°C.
• The heat of fusion of ice is Lf = 3.33×105 J/kg.
• The density of the tea is ρ = 1.00 kg/L.

Part A. In this process, the systems undergo which of the following changes?

A. phase changes only
B. temperature changes only
C. both phase and temperature changes
D. neither phase nor temperature changes

Part B. Determine which quantities are known and which are unknown 

• Initial mass of tea: mtea
• Initial mass of ice: mice 
• initial volume of tea: Vtea
• Initial volume of ice: Vice
• Initial temperature of tea:Ttea
• Initial temperature of ice: Tice
• final temperature of system: Tf

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