Let's look at the heat equation given:
[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]
where:
- [tex]\( q \)[/tex] is the amount of heat energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( C_p \)[/tex] is the specific heat capacity,
- [tex]\( \Delta T \)[/tex] is the change in temperature.
We need to solve for [tex]\( C_p \)[/tex], the specific heat capacity.
To isolate [tex]\( C_p \)[/tex], we need to rearrange the equation:
1. Start with the original equation:
[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]
2. To solve for [tex]\( C_p \)[/tex], divide both sides of the equation by [tex]\( m \cdot \Delta T \)[/tex]:
[tex]\[ \frac{q}{m \cdot \Delta T} = \frac{m \cdot C_p \cdot \Delta T}{m \cdot \Delta T} \][/tex]
3. Simplifying the right side, the [tex]\( m \)[/tex] and [tex]\( \Delta T \)[/tex] cancel out:
[tex]\[ \frac{q}{m \cdot \Delta T} = C_p \][/tex]
So, the correct rearrangement of the heat equation to solve for specific heat capacity [tex]\( C_p \)[/tex] is:
[tex]\[ C_p = \frac{q}{m \cdot \Delta T} \][/tex]
Therefore, the correct answer from the given options is:
[tex]\[ C_p = \frac{q}{m \cdot \Delta T} \][/tex]
