Answer to Question #180745 in Molecular Physics | Thermodynamics for Tobias Amukwiita

Question

An aluminum block (c= 9.1×10^2J/kg K) of mass 0.50 kg at temperature of 155°C is dropped into an aluminum calorometer cup of mass 0.200 kg containing 1.00 kg of water (c=4.2×10^3 J/kg K) at 20°C. The system is insulated and attains equilibrium at a final temperature Tf. a) Using the definition of specific heat capacity, set up the Qtotal = equation. b) solve for Tf.

Answer 1

$Q_1=|Q_2+Q_3|,$

$c_1m_1(t_1-t_f)=c_2m_2(t_f-t_2)+c_1m_3(t_f-t_2),\implies$

$t_f=\frac{c_1m_1t_1+c_2m_2t_2+c_1m_3t_2}{c_1m_1+c_2m_2+c_1m_3},$

$t_f=\frac{910\cdot 0.5\cdot155+4200\cdot1\cdot20+910\cdot0.2\cdot20}{910\cdot0.5+4200\cdot1+910\cdot0.2}=32.7°C.$