One piece of copper jewelry at 101°C has twice the mass of another piece, which is at 38.0°C. Both pieces are placed inside a calorimeter of negligible heat capacity. What is the final temperature inside the calorimeter (c of copper=0.387 j/g.k)?

Respuesta :

Answer:

80.0°C will be the final temperature inside the calorimeter.

Explanation:

Heat lost by  the pace of jewelry  will be equal to heat gained by the another piece of the jewelry

[tex]-Q_1=Q_2[/tex]

Mass of piece-1= [tex]m_1=2m[/tex]

Specific heat capacity of copper= [tex]c [/tex]  = 0.387 J/g.K

Initial temperature of the iron = [tex]T_1=101^oC[/tex]

Final temperature = [tex]T_2[/tex]=T

[tex]Q_1=m_1c_1\times (T-T_1)[/tex]

Mass of piece-2= [tex]m_2=m[/tex]

Specific heat capacity of copper = [tex]c[/tex]  = 0.387 J/g.K

Initial temperature of the water = [tex]T_3=38.0^oC[/tex]

Final temperature of water = [tex]T_2[/tex]=T

[tex]Q_2=m_2c_2\times (T-T_3)[/tex]

[tex]-Q_1=Q_2[/tex]  (conservation of energy)

[tex]-(m_1c_1\times (T-T_1))=m_2c_2\times (T-T_3)[/tex]

On substituting all values:

[tex]-(2mc\times (T-101^oC))=mc\times (T-38.0^oC)[/tex]

[tex]T= 80.0^oC[/tex]

80.0°C will be the final temperature inside the calorimeter.