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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?

Respuesta :

Answer : The temperature of water is, [tex]57.7^oC[/tex]

Explanation :

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

[tex]q_1=-q_2[/tex]

[tex]m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)[/tex]

where,

[tex]c_1[/tex] = specific heat of thermometer = [tex]804J/kg.^oC=0.804J/g^oC[/tex]

[tex]c_2[/tex] = specific heat of water = [tex]4.18J/g.^oC[/tex]

[tex]m_1[/tex] = mass of thermometer = 33.0 g

[tex]m_2[/tex] = mass of water = 149 g

[tex]T_f[/tex] = final temperature = [tex]56.0^oC[/tex]

[tex]T_1[/tex] = initial temperature of thermometer = [tex]15.4^oC[/tex]

[tex]T_2[/tex] = initial temperature of water = ?

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

[tex]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[/tex]

[tex]T_2=57.7^oC[/tex]

Therefore, the temperature of water is, [tex]57.7^oC[/tex]

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