Answer
(a) The heat capacity of the system is $382~J/C^{\circ}$
(b) The heat capacity of the system is $32,070~J/C^{\circ}$
Work Step by Step
(a) The heat capacity $C$ is the amount of heat required to raise the temperature by $1~ C^{\circ}$. We can find the heat capacity of the system:
$C = m_w~c_w+m_b~c_b$
$C = (0.050~kg)(4186~J/kg~C^{\circ})+(0.450~kg)(384~J/kg~C^{\circ})$
$C = 382~J/C^{\circ}$
The heat capacity of the system is $382~J/C^{\circ}$
(b) The heat capacity $C$ is the amount of heat required to raise the temperature by $1~ C^{\circ}$. We can find the heat capacity of the system:
$C = m_w~c_w+m_a~c_a$
$C = (7.5~kg)(4186~J/kg~C^{\circ})+(0.75~kg)(900~J/kg~C^{\circ})$
$C = 32,070~J/C^{\circ}$
The heat capacity of the system is $32,070~J/C^{\circ}$
