Answer to Question #142262 in Molecular Physics | Thermodynamics for Victor Muwadia

Question

A copper calorimeter that weighs 300g contains 200g Oil initially at 293.15K. 180g of Aluminium at 300°C is added to the oil. What will be the final temperature of the system after equilibrium is established?

Specific heat capacity for Copper = 0.379J/g°C

Specific heat capacity for Aluminium= 0.921J/g°C

Specific heat capacity for Oil= 1.54 J/g°C

Answer 1

$m_c = 300g\\ m_o = 200g\\ T_c = 293.15K = 20°C\\ T_o = 20°C\\ m_a = 180g\\ T_a = 300°C\\ T_{final} = ?$

$c_c = 0.379\ J/g°C\\ c_a = 0.921\ J/g°C\\ c_o = 1.54\ J/g°C$

According to the Law of conservation of energy,

Heat gained by substance A = Heat lost by substance B

$\rightarrow m_c c_c (T_f - T_c) + m_o c_o (T_f - T_o) = m_a c_a (T_a T_f)\\ \rightarrow 300×0.379(T_f -20) + 200×1.54(T_f-20) = 180×0.921(300-T_f)\\ \rightarrow 113.7(T_f-20) + 308(T_f-20) = 165.78(300-T_f)\\ \rightarrow (113.7+308)(T_f-20)= 49734-165.78T_f\\ \rightarrow 421.7(T_f-20)= 49734-165.78T_f\\ \rightarrow 421.7T_f - 8434=49734-165.78T_f\\ \rightarrow 587.48T_f = 58168\\ \rightarrow T_f = 99.01°C$

$\therefore$ The final temperature of the system after equilibrium is established will be $99.01°C$