The specific heat capacity of the metal is [tex]1.270 J/(g^{\circ}C)[/tex]
Explanation:
The metal and the water reaches thermal equilibrium when their final temperature is the same (which is [tex]T_f = 21^{\circ}C[/tex], in this problem), and the amount of energy given off by the water is equal to the amount of energy absorbed by the metal.
The amount of energy given off by the water (and absorbed by the metal) is given by[tex]Q=m_w C_w \Delta T[/tex]
where
[tex]m_w = 200 g[/tex] is the mass of water
[tex]C_w = 4.18 J/gC[/tex] is the specific heat capacity of water
[tex]\Delta T = 21-15 = 6^{\circ}C[/tex] is the change in temperature of the water
Therefore,
[tex]Q=(200)(4.18)(6)=5016 J[/tex]
The amount of energy absorbed by the metal can be written as
[tex]Q=m_m C_m \Delta T[/tex]
where
[tex]m_m = 50 g[/tex] is the mass of the metal
[tex]C_m[/tex] is the specific heat capacity of the metal
[tex]\Delta T =100-21 = 79^{\circ}C[/tex] is the change in temperature of the metal
Since we know that Q = 5016 J, we can find the specific heat capacity of the metal:
[tex]C_m = \frac{Q}{m_m \Delta T}=\frac{5016}{(50)(79)}=1.270 J/(g^{\circ}C)[/tex]
Learn more about specific heat capacity:
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