A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 8.10kg of water at 30.3°C. During the reaction 89.0kJ of heat flows out of the flask and into the bath.Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is 4.18·J·g−1K−1. Be sure your answer has the correct number of significant digits.°C
Question
A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 8.10kg of water at 30.3°C. During the reaction 89.0kJ of heat flows out of the flask and into the bath.Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is 4.18·J·g−1K−1. Be sure your answer has the correct number of significant digits.°C
Solution
To solve this problem, we need to use the formula for heat transfer:
q = mcΔT
where: q = heat energy (in joules) m = mass (in grams) c = specific heat capacity (in joules per gram per degree Celsius) ΔT = change in temperature (in degrees Celsius)
First, we need to convert the mass of the water from kg to g, because the specific heat capacity is given in J/g·K.
1 kg = 1000 g, so 8.10 kg = 8100 g.
The heat energy transferred to the water bath is given as 89.0 kJ, but we need to convert this to joules because the specific heat capacity is given in J/g·K.
1 kJ = 1000 J, so 89.0 kJ = 89000 J.
Now we can plug these values into the formula and solve for ΔT:
89000 J = 8100 g * 4.18 J/g·K * ΔT
Rearranging the equation to solve for ΔT gives:
ΔT = 89000 J / (8100 g * 4.18 J/g·K) = 2.6°C
The final temperature of the water bath is the initial temperature plus the change in temperature:
30.3°C + 2.6°C = 32.9°C
So, the new temperature of the water bath is 32.9°C.
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