A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 3.90kg of water at 28.0°C. During the reaction 131.kJ of heat flows out of the bath and into the flask.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.
Question
A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 3.90kg of water at 28.0°C. During the reaction 131.kJ of heat flows out of the bath and into the flask.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.
Solution
To solve this problem, we need to use the formula for heat transfer:
q = mcΔT
where: q = heat energy (Joules) m = mass (kg) c = specific heat capacity (J/g·K) ΔT = change in temperature (K)
First, we need to convert the mass of water from kg to g, because the specific heat capacity is given in J/g·K.
m = 3.90 kg = 3900 g
The heat energy q is given as 131 kJ, which we need to convert to J:
q = 131 kJ = 131,000 J
We know that heat is flowing out of the water, so q is negative:
q = -131,000 J
We can now plug these values into the formula and solve for ΔT:
-131,000 J = (3900 g)(4.18 J/g·K)(ΔT)
Solving for ΔT gives:
ΔT = -131,000 J / [(3900 g)(4.18 J/g·K)] = -7.97 K
The change in temperature is negative, which means the temperature of the water decreases.
The initial temperature of the water is 28.0°C. So, the final temperature is:
T_final = T_initial + ΔT = 28.0°C - 7.97°C = 20.03°C
So, the new temperature of the water bath is approximately 20.0°C. This answer has three significant digits, which is appropriate given the number of significant digits in the problem statement.
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