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.

$q_1=-q_2$

$m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)$

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:

$33.0g\times 0.804J/g^oC\times (56.0-15.4)^oC=-149g\times 4.18J/g.^oC\times (56.0-T_2)^oC$

$T_2=57.7^oC$

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