Respuesta :
Answer:
The final temperature of the mixture is = 42.14 °C
Explanation:
Mass of the aluminium [tex]m_{a}[/tex] = 101 gm
Specific heat for aluminium [tex]C_{a}[/tex] = 0.9 [tex]\frac{J}{gm c }[/tex]
Temperature of aluminium [tex]T_{a}[/tex] = 100.1 °C
Mass of water [tex]m_{w}[/tex] = 48.9 gm
Specific heat for water [tex]C_{w}[/tex] = 4.2 [tex]\frac{J}{gm c }[/tex]
Initial temperature of water [tex]T_{w}[/tex] = 16.5 °C
From energy balance principal when the aluminium piece is heated and dropped in to the water , the final temperature of aluminium & the water becomes equal.
From the energy conservation principal
Heat lost from the aluminium piece = heat gain by the water
⇒ [tex]m_{a}[/tex] [tex]C_{a}[/tex] ( [tex]T_{a}[/tex] - [tex]T_{f}[/tex] ) = [tex]m_{w}[/tex] [tex]C_{w}[/tex] ( [tex]T_{f}[/tex] - [tex]T_{w}[/tex] ) ----------- (1)
Put all the values in equation (1)
⇒ 101 × 0.9 × (100.1 - [tex]T_{f}[/tex] ) = 48.9 × 4.2 × ( [tex]T_{f}[/tex] - 16.5 )
⇒ 90.9 × (100.1 - [tex]T_{f}[/tex] ) = 205.38 × ( [tex]T_{f}[/tex] - 16.5 )
⇒ 100.1 - [tex]T_{f}[/tex] = 2.26 ( [tex]T_{f}[/tex] - 16.5 )
⇒ 100.1 - [tex]T_{f}[/tex] = 2.26 [tex]T_{f}[/tex] - 37.28
⇒ 3.26 [tex]T_{f}[/tex] = 137.38
⇒ [tex]T_{f}[/tex] = 42.14 °C
Therefore the final temperature of the mixture is = 42.14 °C
