The specific heat of the unknown sample has been [tex]\rm \bold{0.192\;\;J/g^\circ C}[/tex].
Specific heat has been defined as the amount of heat required to raise the temperature of 1 gram of substance by 1 degree Celsius.
The specific heat (c) for a substance can be given by:
[tex]Q=mc\Delta T[/tex] ......(i)
Where, the heat required by the substance, [tex]Q=345.2\;\text J[/tex]
The mass of the substance has been, [tex]m=89.5\;\text g[/tex]
The change in temperature of the system has been, [tex]\Delta T[/tex]
The change in temperature has been given as:
[tex]\Delta T=T_f-T_i[/tex]
The initial temperature of the substance, [tex]T_i=285\;\text K[/tex]
The final temperature of the substance, [tex]T_f=305\;\text K[/tex]
Substituting the values for the change in temperature, [tex]\Delta T[/tex]:
[tex]\Delta T=305\;-\;285\;K\\\Delta T=20\;\text K[/tex]
Substituting the values in equation (i):
[tex]345.2=89.5\;\times\;c\;\times\;20\\345.2=1,790c\\c=0.192\rm \;J/g^\circ C[/tex]
The specific heat of the unknown sample has been [tex]\rm \bold{0.192\;\;J/g^\circ C}[/tex].
For more information about specific heat, refer to the link:
https://brainly.com/question/2094845