In an experiment to determine the rate at which heat is extracted from a hot material, 305 g of the material at 90 °C is put into a 50 mm diameter copper vessel to a depth of 90 mm as shown below. The hot material and calorimeter are placed in a container holding 189 g of cold water at 22.7 °C. The temperature of the water is then measured every 30 seconds for 3minutes. The results are plotted as in the previous question and the average temperature rise per second is calculated as 0.0065 ± 0.0005 °C/sec.
From the data provided and the graph below, determine the average heat power ( in kW ) transferred to the water - DO NOT INCLUDE THE UNITS IN YOUR ANSWER.
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In an experiment to determine the rate at which heat is extracted from a hot material, 305 g of the material at 90 °C is put into a 50 mm diameter copper vessel to a depth of 90 mm as shown below. The hot material and calorimeter are placed in a container holding 189 g of cold water at 22.7 °C. The temperature of the water is then measured every 30 seconds for 3minutes. The results are plotted as in the previous question and the average temperature rise per second is calculated as 0.0065 ± 0.0005 °C/sec.
From the data provided and the graph below, determine the average heat power ( in kW ) transferred to the water - DO NOT INCLUDE THE UNITS IN YOUR ANSWER.
To determine the average heat power transferred to the water, we need to calculate the heat energy transferred per unit of time. The formula to calculate heat energy is:
Q = mcΔT
Where:
Q = heat energy transferred
m = mass of the substance (water in this case)
c = specific heat capacity of the substance (water)
ΔT = change in temperature
First, we need to calculate the heat energy transferred to the water. We know the mass of the water (189 g) and the change in temperature (ΔT) from the graph. The specific heat capacity of water is approximately 4.18 J/g°C.
Next, we need to convert the heat energy from joules (J) to kilowatts (kW). There are 3,600,000 joules in 1 kilowatt-hour (kWh). Therefore, we divide the heat energy in joules by 3,600,000 to get the heat power in kilowatts.
Let's calculate it step by step:
1. Calculate the heat energy transferred to the water:
Q = mcΔT = (mass of water) × (specific heat capacity of water) × (change in temperature)
Q = 189 g × 4.18 J/g°C × 0.0065 °C/sec
2. Convert the heat energy from joules to kilowatts:
Heat power (kW) = Q / 3,600,000 J/kWh
Now, we can plug in the values and calculate the heat power transferred to the water.