A student mixes 95.1g of water at 77.5 degree C with 42.7g of water at 141.1 degree C in an insulated flask. What is the final temperature of the combined water?
heat lost by one sample + heat gained by the other sample = 0
[mass water1 x (Tfinal-Tinitial)] + [mass water 2 x (Tfinal-Tinitial)] = 0
Solve for Tfinal.
fxv
How many joules of heat energy are absorbed when 100 grams of water are heated from 20 degrees Celsius to 30 degrees Celsius?
To find the final temperature of the combined water, we can use the principle of conservation of energy. The total heat gained by the cooler water should be equal to the total heat lost by the hotter water.
The equation for heat transfer can be given as:
q = mcΔT
Where:
q = heat transferred
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
First, let's calculate the heat lost by the hot water:
q1 = m1c1ΔT1
Where:
m1 = mass of the hot water
c1 = specific heat capacity of water (4.18 J/g °C)
ΔT1 = change in temperature of the hot water
m1 = 42.7g
c1 = 4.18 J/g °C
ΔT1 = 141.1°C - Tf (Final temperature)
Next, let's calculate the heat gained by the cold water:
q2 = m2c2ΔT2
Where:
m2 = mass of the cold water
c2 = specific heat capacity of water (4.18 J/g °C)
ΔT2 = change in temperature of the cold water
m2 = 95.1g
c2 = 4.18 J/g °C
ΔT2 = Tf - 77.5°C
According to the principle of conservation of energy, the heat lost by the hot water should be equal to the heat gained by the cold water:
q1 = q2
m1c1ΔT1 = m2c2ΔT2
Substituting the given values:
(42.7g)(4.18 J/g °C)(141.1°C - Tf) = (95.1g)(4.18 J/g °C)(Tf - 77.5°C)
Now, we can simplify the equation and solve for Tf.
First, let's distribute the values:
(42.7g)(4.18 J/g °C)(141.1°C - Tf) = (95.1g)(4.18 J/g °C)(Tf - 77.5°C)
Next, let's multiply and simplify:
(178.6666)(141.1 - Tf) = (397.518)(Tf - 77.5)
25234.6126 - 178.6666Tf = 397.518Tf - 30817.985
Combine like terms:
178.6666Tf + 397.518Tf = 25234.6126 + 30817.985
576.1846Tf = 56052.5976
Now, divide both sides by 576.1846 to solve for Tf:
Tf = 56052.5976 / 576.1846
Tf ≈ 97.24°C
Therefore, the final temperature of the combined water is approximately 97.24°C.