Which of the following shows the correct rearrangement of the heat equation [tex] q = m C_p \Delta T [/tex] to solve for specific heat?

A. [tex] C_p = m q \Delta T [/tex]
B. [tex] C_p = \frac{q m}{\Delta T} [/tex]
C. [tex] C_p = \frac{q}{m \Delta T} [/tex]



Answer :

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]