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 33.0 g, a specific heat capacity of c = 804 J/(kg C°), and a temperature of 15.4 °C. It is immersed in 149 g of water, and the final temperature of the water and thermometer is 56.0 °C. What was the temperature of the water in degrees Celsius before the insertion of the thermometer?

Answer 1

Answer : The temperature of water is,
`57.7^oC`

Explanation :

In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.

`q_1=-q_2`

`m_1* c_1* (T_f-T_1)=-m_2* c_2* (T_f-T_2)`

where,

`c_1` = specific heat of thermometer =
`804J/kg.^oC=0.804J/g^oC`

`c_2` = specific heat of water =
`4.18J/g.^oC`

`m_1` = mass of thermometer = 33.0 g

`m_2` = mass of water = 149 g

`T_f` = final temperature =
`56.0^oC`

`T_1` = initial temperature of thermometer =
`15.4^oC`

`T_2` = initial temperature of water = ?

Now put all the given values in the above formula, we get:

`33.0g* 0.804J/g^oC* (56.0-15.4)^oC=-149g* 4.18J/g.^oC* (56.0-T_2)^oC`

`T_2=57.7^oC`

Therefore, the temperature of water is,
`57.7^oC`