Mass of copper ball $(m_b) = 400 \; gm = 0.4 \; kg$
Mass of calorimeter $(m_c) = 300 \; gm = 0.3 \;kg$
Mass of water $(m_w) = 1 \; kg$
Initial temp of water and calorimeter $(θ_2) = 20^{\circ}C$
Final temp $(θ) = 50^{\circ}C $
Specific heat capacity of copper ball $(S_c) = 400 \; J / Kg K $
Specific heat capacity of water $(S_w) = 4200 \; J / Kg C $
Temperature of ball $(θ_1) = ?$
From the principle of calorimetry,
Heat loss = Heat gain
$m_b \; S_c (\theta_1 - \theta) = (m_c \; S_c + m_w \; S_w) \; (\theta - \theta_2)$
From the principle of calorimetry,
Heat loss = Heat gain
$m_b \; S_c (\theta_1 - \theta) = (m_c \; S_c + m_w \; S_w) \; (\theta - \theta_2)$
or, $0.4 * 400 (\theta_1 - 50) = 0.3 * 400 * + 1 * 4200) \; (50 - 20)$
or, $160 (\theta_1 - 50) = 129600$
or, $\theta_1 = 810 + 50 = 860^{\circ}C$
$\therefore$ Temperature of ball is $860^{\circ}C$
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