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.

Question

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.

Answer 1

To determine the rate at which heat is extracted from the hot material, we need to calculate the heat transfer rate or the rate of change of temperature over time.

First, let's find the mass of the water in the container. Given that the weight of the cold water is 189 g, we can assume it is equivalent to its mass, since the density of water is approximately 1 g/mL.

Next, we need to determine the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 J/g·°C. Specific heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 °C per gram (J/g·°C).

To calculate the heat energy transferred from the hot material to the water, we can use the formula:

Q = m * c * ΔT

where:
Q is the heat energy transferred (in joules),
m is the mass of the water (in grams),
c is the specific heat capacity of water (in J/g·°C), and
ΔT is the change in temperature (in °C).

Since we are given the average temperature rise per second (0.0065 ± 0.0005 °C/sec), we can multiply it by the time in seconds to get the change in temperature.

ΔT = (0.0065 ± 0.0005 °C/sec) * (3 * 60 seconds)

Now we have all the required information to calculate the heat energy transferred from the hot material to the water.

Let's plug in the values:

Q = 189 g * 4.18 J/g·°C * ΔT

Calculate ΔT:

ΔT = (0.0065 ± 0.0005 °C/sec) * (3 * 60 seconds)

Substitute the value of ΔT into the equation:

Q = 189 g * 4.18 J/g·°C * (0.0065 ± 0.0005 °C/sec) * (3 * 60 seconds)

To find the rate at which heat is extracted, we need to divide the heat energy transferred (Q) by the total time (3 minutes) in seconds.

Heat transfer rate = Q / (3 * 60 seconds)

Calculating this value will give us the rate at which heat is extracted from the hot material.