Consider an isolated system composed of two thermodynamic system components, A and $B,$ in thermal contact and each at different initial temperatures and $T_{i,B}).$ The nonzero heat $(q)$ transferred into or out of each system can be related across the systems by:

$q_A=-q_B$

where each heat transfer can be expressed as:

$q_A=m_A*C_{s,A}*T_A$ and $q_B=m_B*C_{s,B}*T_B$

In the above expressions, $m_x$ is the mass of system component $x($where $x=A$ or $B),C_{s,x}$ is the specific heat capacity of component $x,$ and $T_x$ is the temperature change from the initial conditions to thermal equilibrium for component $x.$ Note that $T_x=T_{f,x}-T_{i,x}$ where $f$ and i indicate the final and initial temperatures of component $x,$ respectively.

Label each of the following mathematical statements as true or false given $q_A=-q_B,q_x=m_x*C_{s,x}*T_x,$ and $T_x=T_{f,x}-T_{i,x}$ are true.

$(1)m_A*C_{s,A}*T_A=-m_B*C_{s,B}*T_B$

$(2)q_A=-m_B*C_{s,B}*T_B,$ choose your answer... $vv$

$(3)m_A*C_{s,A}*(T_{f,A}-T_{i,A})=-m_B*C_{s,B}*(T_{f,B}-T_{i,B})$

$(4)-T_A*C_{s,A}*m_A=C_{s,B}*m_B*T_B$

$(5)m_A*C_{s,A}*T_{f,A}-m_A*C_{s,A}*T_{i,A}=-m_B*C_{s,B}*T_{f,B}+m_B*C_{s,B}*T_{i,B},$ choose your answer... $vv$

$(6)m_A*C_{s,A}*T_{f,A}+m_B*C_{s,B}*T_{f,B}=m_A*C_{s,A}*T_{i,A}+m_B*C_{s,B}*T_{i,B},$ choose your answer...