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A sample ofpolystyrene, which has a specific heat capacity of 1.880 J/g K, is put into a calorimeter that contains 100.0 g of water. The polystyrene sample starts off at 89.8 C and the temperature of water starts off at 19.0°C. When the temperature of the water stops changing it is 33.5°C. The pressure remains constant at 1.0 atm. Calculate the mass of the polystyrene sample. Be sure your answer is rounded to significant digits.

Respuesta :

Answer : The mass of the polystyrene sample is 57.3 grams.

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 polystyrene = [tex]1.880J/g^oC[/tex]

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

[tex]m_1[/tex] = mass of polystyrene = ?

[tex]m_2[/tex] = mass of water = 100.0 g

[tex]T_f[/tex] = final temperature of system = [tex]33.5^oC[/tex]

[tex]T_1[/tex] = initial temperature of polystyrene = [tex]89.8^oC[/tex]

[tex]T_2[/tex] = initial temperature of water = [tex]19.0^oC[/tex]

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

[tex]m_1\times 1.880J/g^oC\times (33.5-89.8)^oC=-100g\times 4.18J/g^oC\times (33.5-19.0)^oC[/tex]

[tex]m_1=57.3g[/tex]

Therefore, the mass of the polystyrene sample is 57.3 grams.

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