A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 5.10kg of water at 24.3°C. During the reaction 125.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 5.10kg of water at 24.3°C. During the reaction 125.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 = 5.10 kg = 5100 g
The heat energy transferred is given as 125 kJ, we need to convert this to Joules:
q = 125 kJ = 125,000 J
We know that heat is being transferred out of the water, so q is negative:
q = -125,000 J
We can now rearrange the formula to solve for ΔT:
ΔT = q / (mc)
Substituting the known values:
ΔT = -125,000 J / (5100 g * 4.18 J/g·K)
ΔT = -5.99 K
The change in temperature is negative, which means the temperature of the water decreases.
The initial temperature of the water is 24.3°C. To find the final temperature, we subtract the change in temperature:
T_final = T_initial - ΔT
T_final = 24.3°C - (-5.99°C)
T_final = 30.29°C
So, the final temperature of the water bath is 30.29°C. This answer has 4 significant digits, which is appropriate given the number of significant digits in the problem statement.
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