Answer: The specific heat of given metal is [tex]1.195 J/^{o}C[/tex].
Explanation:
Given: Mass of sample = 22.8 g
Heat energy = 1450 J
Initial temperature = [tex]21.8^{o}C[/tex]
Final temperature = [tex]75^{o}C[/tex]
Formula used to calculate the specific heat is as follows.
[tex]q = m \times C \times (T_{2} - T_{1})[/tex]
where,
q = heat energy
m = mass of substance or sample
C = specific heat
[tex]T_{1}[/tex] = initial temperature
[tex]T_{2}[/tex] = final temperature
Substitute the values into above formula as follows.
[tex]q = m \times C \times (T_{2} - T_{1})\\1450 J = 22.8 g \times C \times (75 - 21.8)^{o}C\\C = \frac{1450 J}{22.8 \times 53.2^{o}C}\\= 1.195 J/^{o}C[/tex]
Thus, we can conclude that the specific heat of given metal is [tex]1.195 J/^{o}C[/tex].
