Question

A 22 g block of ice is cooled to −68◦C. It is added to 521g of water in an 67g copper calorimeter at a temperature of 21◦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 is4186J/kg·◦C.

Answer in units of ◦C.

Answer 1

Let us denote the final unknown temperature as $t$, and initial temperature of water/calorimeter and ice $t_0, t_i$ respectively. Heat balance equation is:

$m_w c_w(t - t_0) + m_c c_c(t - t_0) + m_i c_i (t - t_i) + \lambda m_i = 0$ (notation indices $w, c, i$ correspond to water, copper and ice respectively).

From the last formula, $t = \frac{m_w c_w t_0 + m_c c_c t_0 + m_i c_i t_i - \lambda m_i}{m_w c_w + m_c c_c + m_i c_i} \approx 15.9^{\circ}C$.