Ideally, when a thermometer is used to measure the temperature of an object, the temperature of the object itself should not change. However, if a significant amount of heat flows from the object to the thermometer, the temperature will change. A thermometer has a mass of 31.2 g, a specific heat capacity of c = 815 J/(kg C°), and a temperature of 13.6 °C. It is immersed in 148 g of water, and the final temperature of the water and thermometer is 53.8 °C. What was the temperature of the water in degrees Celsius before the insertion of the thermometer?

Question

Ideally, when a thermometer is used to measure the temperature of an object, the temperature of the object itself should not change. However, if a significant amount of heat flows from the object to the thermometer, the temperature will change. A thermometer has a mass of 31.2 g, a specific heat capacity of c = 815 J/(kg C°), and a temperature of 13.6 °C. It is immersed in 148 g of water, and the final temperature of the water and thermometer is 53.8 °C. What was the temperature of the water in degrees Celsius before the insertion of the thermometer?

Answer 1

To solve this problem, we can use the principle of conservation of energy. The heat lost by the water in the system is equal to the heat gained by the thermometer. The equation we can use is:

heat lost by water = heat gained by thermometer

We can calculate the heat lost by the water using the equation:

Q1 = m1 * c1 * (T2 - T1)

Where:
Q1 is the heat lost by the water
m1 is the mass of the water (148 g)
c1 is the specific heat capacity of water (approximately 4.18 J/(g°C))
T2 is the final temperature of the system (53.8 °C)
T1 is the initial temperature of the water (unknown)

We can calculate the heat gained by the thermometer using the equation:

Q2 = m2 * c2 * (T2 - T1)

Where:
Q2 is the heat gained by the thermometer
m2 is the mass of the thermometer (31.2 g)
c2 is the specific heat capacity of the thermometer (815 J/(kg°C))
T2 is the final temperature of the system (53.8 °C)
T1 is the initial temperature of the thermometer (13.6 °C)

Since the temperature changes are given in degrees Celsius, we can simply use the temperature values without converting them to Kelvin.

Now, let's calculate the heat lost by the water:

Q1 = m1 * c1 * (T2 - T1)
Q1 = 148g * 4.18 J/(g°C) * (53.8°C - T1)

And the heat gained by the thermometer:

Q2 = m2 * c2 * (T2 - T1)
Q2 = 31.2g * 815 J/(kg°C) * (53.8°C - 13.6°C)

Since the heat lost by the water is equal to the heat gained by the thermometer, we can set up the equation:

Q1 = Q2

148g * 4.18 J/(g°C) * (53.8°C - T1) = 31.2g * 815 J/(kg°C) * (53.8°C - 13.6°C)

Now, we can solve for the initial temperature of the water (T1). By simplifying and rearranging the equation, we can find the value of T1.