$${c_\text{k} =- \frac{c_\text{v} m_\text{v} (t^\circ - t^\circ_\text{v}) + c_\text{Al} m_\text{t} (t^\circ - t^\circ_\text{t1})}{m_\text{k} (t^\circ -t^\circ_\text{k1})}}$$