Answer: [tex]T=26.36^{\circ}C[/tex]
Explanation:
Given
mass of the first object [tex]m_1=5\ kg[/tex]
mass of the second object [tex]m_2=0.5\ kg[/tex]
specific heat of the two is [tex]c_1=c_2=4200\ J/kg/^{\circ}C[/tex]
The temperature of the first [tex]T_1=20^{\circ}[/tex]
The temperature of the second [tex]T_2=90^{\circ}[/tex]
Heat flows from high temperature to low temperature
Suppose T is the common temperature
[tex]m_1c_1(T-T_1)=m_2c_2(T_2-T)\\5\times 4200\times (T-20)=0.5\times 4200\times (90-T)\\5T-100=45-0.5T\\5.5T=145\\T=26.36^{\circ}C[/tex]
