Answer to Question #109889 in Molecular Physics | Thermodynamics for Martin

Question

What mass of ice at -14 Celsius will be needed to cool 200cm cube of an orange drink from 25 Celsius to 10 Celsius.( Specific fusion of ice= 3.36×10^5.specific heat capacity of ice= 2100. Specific heat capacity of water= 4200Jkg^-1

Answer 1

$$m_i(L+c_i(T_0-T_i)+c_w(T-T_0))=m_wc_w(T_w-T)$$

$$m_i=\rho V_w\frac{c_w(T_w-T)}{L+c_i(T_0-T_i)+c_w(T-T_0)}$$

$$m_i=\frac{(1000)(200\cdot10^{-6})(4200)(25-10)}{3.36\cdot10^{5}+2100(0-(-14))+4200(10-0)}$$

$$m_i=0.031\ kg=31\ g$$