The final temperature of the mixture is about 28.8°C
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Specific Heat Capacity is the amount of energy needed to raise temperature of 1 kg body for 1°C.
[tex]\large {\boxed{Q = m \times c \times \Delta t} }[/tex]
Q = Energy ( Joule )
m = Mass ( kg )
c = Specific Heat Capacity ( J / kg°C )
Δt = Change In Temperature ( °C )
Let us now tackle the problem!
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Given:
initial temperature of water = t₁ = 20.9°C
specific heat capacity of water = c = 4.186 J/gK
mass of copper = m₁ = 155.0 g
mass of water = m₂ = 250.0 g
initial temperature of copper = t₁' = 168°C
specific heat capacity of copper = c' = 0.385 J/gK
Asked:
final temperature of the mixture = t = ?
Solution:
We can calculate the final temperature of the water by using Conservation of Energy as shown below:
[tex]Q_{lost} = Q_{gain}[/tex]
[tex]m_1c'(t_1' - t) = m_2c(t - t_1)[/tex]
[tex]155(0.385)(168 - t) = 250(4.186)(t - 20.9)[/tex]
[tex]59.675(168 - t) = 1046.5(t - 20.9)[/tex]
[tex]10025.4 - 59.675t = 1046.5t - 21871.85[/tex]
[tex]t = ( 10025.4 + 21871.85 ) \div ( 59.675 + 1046.5 )[/tex]
[tex]t \approx 28.8^oC[/tex]
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Grade: College
Subject: Physics
Chapter: Thermal Physics
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Keywords: Heat , Temperature , Block , Aluminium , Ice , Cold , Water
