Derivation

We'll start off spice$-$free. This first example is just an exercise in basic arithmetic operations $($multiplication$,$ division, addition, and subtraction$)$ and algebraic methods of

solving simple equations. You can probably deduce the answers after one attempt, but make sure you can actually derive each expression! You will be expected to do this

kind of math in this class.

Consider an isolated system composed of two thermodynamic system components, A and $B,$ in thermal contact and each at different initial temperatures. The nonzero heat

$($q$)$ transferred into or out of each system can be related across the systems by:

$q_A=-q_B$

Label each of the following mathematical statements as true or false given $q_A=-q_B$ is true.

$(1)-q_A=q_B$

choose your answer...

$(2)\frac{q_A}{q_B}=-1$

$(3)-\frac{q_A}{q_B}=1$

choose your answer...

$(4)-q_A-q_B=0$

choose your answer...

$(5)\frac{q_A}{q_B}+1=0$

$(6)\frac{q_A+q_B}{q_B}=0$

choose your answer...