Question

Explain as you were teaching step by step think of this like you are speaking while teaching the solution to someone else. What would you say to help someone understand each step? Write it out clearly, showing all the formulas , and illustrations

1. A thermometer of mass 0.055 kg and heat capacity 46.1 J/K reads 15.0°C. It is then completely immersed in 0.300 kg of water and it comes to the same final temperature as the water. If the thermometer reads 44.4°C, what was the temperature of the water before insertion of the thermometer, neglecting other heat losses?

Answer 1

To find the initial temperature of the water, we can use the concept of heat transfer. Since the thermometer and the water reach the same final temperature, we can assume that the heat gained by the water is equal to the heat lost by the thermometer. By using the formulas for heat transfer and substituting the given values, we can calculate the initial temperature of the water to be 10.67°C.

Step-by-step explanation:

To find the initial temperature of the water, we can use the concept of heat transfer. Since the thermometer and the water reach the same final temperature, we can assume that the heat gained by the water is equal to the heat lost by the thermometer.

First, we calculate the heat gained by the water using the formula:

Q = mcΔT

Where Q is the heat gained, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Next, we calculate the heat lost by the thermometer using the formula:

Q = mcΔT

Where Q is the heat lost, m is the mass of the thermometer, c is the specific heat capacity of the thermometer, and ΔT is the change in temperature.

Since the heat gained and the heat lost are equal, we can set up the following equation:

mwcwΔTw = mtctΔTt

Solving for the initial temperature of the water:

Twi = Ttf - (ΔTt * ct / cw)

Substituting the given values:

Twi = 44.4°C - (29.4°C * 46.1 J/K / (4.18 J/g°C * 0.300 kg))

Twi = 44.4°C - 33.73°C

Twi = 10.67°C