1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Question 16A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 9.10kg of water at 24.3°C. During the reaction 68.3kJ 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.
Question
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Question 16A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 9.10kg of water at 24.3°C. During the reaction 68.3kJ 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.
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 kg) c = specific heat capacity (in J/g·K) ΔT = change in temperature (in 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.
So, m = 9.10 kg = 9100 g
The heat energy q is given as 68.3 kJ, we need to convert it to Joules:
q = 68.3 kJ = 68300 J
We can now rearrange the formula to solve for ΔT:
ΔT = q / (mc)
Substituting the given values:
ΔT = 68300 J / (9100 g * 4.18 J/g·K) = 1.75 K
So, the change in temperature of the water bath is 1.75°C.
The initial temperature of the water bath is 24.3°C, so the final temperature will be:
T_final = T_initial + ΔT = 24.3°C + 1.75°C = 26.05°C
So, the new temperature of the water bath is 26.05°C.
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