Answer:
T = 20.84°C
Explanation:
From the law of conservation of energy:
Heat Lost by Copper Block = Heat Gained by Aluminum Calorimeter + Heat Gained by Water
[tex]m_cC_c\Delta T_c = m_wC_w\Delta T_w + m_aC_a\Delta T_a[/tex]
where,
[tex]m_c[/tex] = mass of copper = 227 g
[tex]m_w[/tex] = mass of water = 844 g
[tex]m_a[/tex] = mass of aluminum = 155 g
[tex]C_c[/tex] = specific heat capacity of calorimeter = 385 J/kg.°C
[tex]C_w[/tex] = specific heat capacity of water = 4200 J/kg.°C
[tex]C_a[/tex] = specific heat capacity of aluminum = 890 J/kg.°C
[tex]\Delta T_c[/tex] = change in temperature of copper = 283°C - T
[tex]\Delta T_w[/tex] = change in temperature of water = T - 14.6°C
[tex]\Delta T_a[/tex] = change in temperature of aluminum = T - 14.6°C
T = equilibrium temperature = ?
Therefore,
[tex](227\ g)(385\ J/kg.^oC)(283^oC-T)=(844\ g)(4200\ J/kg.^oC)(T-14.6^oC)+(155\ g)(890\ J/kg.^oC)(T-14.6^oC)\\\\24732785\ J - (87395\ J/^oC) T = (3544800\ J/^oC) T - 51754080\ J+ (137950\ J/^oC) T-2014070\ J\\\\24732785\ J +51754080\ J+2014070\ J = (3544800\ J/^oC) T+(137950\ J/^oC+(87395\ J/^oC) T\\\\78560935\ J = (3770145\ J/^oC) T\\\\T = \frac{78560935\ J}{3770145\ J/^oC}[/tex]
T = 20.84°C
