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 30.3 g, a specific heat capacity of c = 827 J/(kg C°), and a temperature of 11.9 °C. It is immersed in 128 g of water, and the final temperature of the water and thermometer is 41.8 °C. What was the temperature of the water in degrees Celsius before the insertion of the thermometer?

Answer 1

Answer : The initial temperature of the water was $43.2^oC$

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 = $827J/kg.^oC$

$c_2$ = specific heat of water = $4184J/kg.^oC$

$m_1$ = mass of thermometer = 30.3 g

$m_2$ = mass of water = 128 g

$T_f$ = final temperature of water and thermometer = $41.8^oC$

$T_1$ = initial temperature of thermometer = $11.9^oC$

$T_2$ = initial temperature of water = ?

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

$30.3g\times 827J/kg.^oC\times (41.8-11.9)^oC=-128g\times 4184J/kg.^oC\times (41.8-T_2)^oC$

$T_2=43.2^oC$

Therefore, the initial temperature of the water was $43.2^oC$