Question

A 31 g block of ice is cooled to −63 ◦C. It is added to 524 g of water in an 66 g copper calorimeter at a temperature of 26◦C. Find the final temperature. The specific heat of copper is 387 J/kg · ◦C and of ice is 2090 J/kg · ◦C . The latent heat of fusion of water is 3.33 × 105 J/kg and its specific heat is 4186 J/kg · ◦C . Answer in units of ◦C.

Answer 1

$m_1C_1(0-T_1) - ice\ heating\ to \ 0^oC\\ m1\lambda - ice\ melting\\ m_1C_2(T-0) - melted\ water\ heating\ \\ m_2C_2(T-T_2) - water\ cooling\\ m_3C_3(T-T_3) - copper\ cooling$

$m_1C_1(0-T_1)+m1\lambda+m_1C_2(T-0)+m_2C_2(T-T_2)+m_3C_3(T-T_3)=0\\$

$0.031 · 2090 · 63+0.031 · 3.33 · 10^5+0.031 · 4186 · T+0.589 · 2090· (T-26)+0.066·387· (T-26) =0$

$1386.328 · T=18265.582\\ T=13.18^oC$

Answer: $T=13.18^oC$.