A filled paddling pool was outside for an hour on a warm sunny day.During this time 2.81 MJ of energy was transferred to the 167 kg of water that started at 15.3 °C.Calculate the temperature of the water at the end of the hour.The specific heat capacity of water is 4200 J/kg°C._____ °CYou do not need to include units in your answer.Give your answer to 3 significant figures.I DON'T KNOWSUBMIT ANSWER
Question
A filled paddling pool was outside for an hour on a warm sunny day.During this time 2.81 MJ of energy was transferred to the 167 kg of water that started at 15.3 °C.Calculate the temperature of the water at the end of the hour.The specific heat capacity of water is 4200 J/kg°C._____ °CYou do not need to include units in your answer.Give your answer to 3 significant figures.I DON'T KNOWSUBMIT ANSWER
Solution
First, we need to convert the energy from MJ to J because the specific heat capacity of water is given in J/kg°C.
1 MJ = 1,000,000 J
So, 2.81 MJ = 2.81 * 1,000,000 = 2,810,000 J
The formula to calculate the change in temperature is:
ΔT = Q / (m * c)
where: ΔT is the change in temperature, Q is the heat energy transferred, m is the mass of the substance, and c is the specific heat capacity of the substance.
Substituting the given values into the formula:
ΔT = 2,810,000 J / (167 kg * 4200 J/kg°C) = 0.399 °C
The final temperature of the water is the initial temperature plus the change in temperature:
T_final = T_initial + ΔT = 15.3 °C + 0.399 °C = 15.699 °C
Rounded to three significant figures, the final temperature of the water is 15.7 °C.
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