To solve for the mass [tex]\( m \)[/tex] in the equation [tex]\( q = m C dT \)[/tex], we need to isolate [tex]\( m \)[/tex]. Here is the step-by-step solution:
1. Start with the initial equation given:
[tex]\[
q = m C dT
\][/tex]
2. To isolate [tex]\( m \)[/tex], we need to divide both sides of the equation by [tex]\( C dT \)[/tex]. This can be shown as multiplying by the reciprocal of [tex]\( C dT \)[/tex]:
[tex]\[
q \times \frac{1}{C dT} = m C dT \times \frac{1}{C dT}
\][/tex]
3. On the right side, the [tex]\( C dT \)[/tex] terms cancel out:
[tex]\[
q \times \frac{1}{C dT} = m
\][/tex]
4. Simplifying the left side:
[tex]\[
\frac{q}{C dT} = m
\][/tex]
Thus, the mass [tex]\( m \)[/tex] can be expressed as:
[tex]\[
m = \frac{q}{C dT}
\][/tex]
To directly answer the specific parts of the question:
- The expression to multiply both sides of the equation by is:
[tex]\[
\boxempty = \frac{1}{C dT}
\][/tex]
- The resulting equation to solve for [tex]\( m \)[/tex] is:
[tex]\[
m = \frac{q}{C dT}
\][/tex]
