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A sample of an unknown substance has a mass of 0.465 kg. If 3,000.0 J of heat is required to heat the substance from 50.0°C to 100.0°C, what is the specific heat of the substance?

Use [tex]\( q = m C_p \Delta T \)[/tex].

A. [tex]\(0.00775 \, \text{J}/(g \cdot °C)\)[/tex]
B. [tex]\(0.0600 \, \text{J}/(g \cdot °C)\)[/tex]
C. [tex]\(0.129 \, \text{J}/(g \cdot °C)\)[/tex]
D. [tex]\(0.155 \, \text{J}/(g \cdot °C)\)[/tex]

Sagot :

GinnyAnswer
To determine the specific heat ([tex]\(C_p\)[/tex]) of the substance, we can use the formula:

[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]

where:
- [tex]\( q \)[/tex] is the heat added (in Joules),
- [tex]\( m \)[/tex] is the mass of the substance (in kg or g),
- [tex]\( C_p \)[/tex] is the specific heat capacity (in [tex]\( \text{J/g}^\circ\text{C} \)[/tex]),
- [tex]\(\Delta T \)[/tex] is the change in temperature (in [tex]\(^\circ\text{C}\)[/tex]).

Let’s break this down step-by-step:

1. Identify given values:
- [tex]\( q = 3000.0 \text{ J} \)[/tex]
- [tex]\( m = 0.465 \text{ kg} \)[/tex]
- Initial temperature = [tex]\( 50.0^\circ \text{C} \)[/tex]
- Final temperature = [tex]\( 100.0^\circ \text{C} \)[/tex]

2. Calculate the temperature change ([tex]\(\Delta T\)[/tex]):
[tex]\[ \Delta T = 100.0^\circ\text{C} - 50.0^\circ\text{C} = 50.0^\circ\text{C} \][/tex]

3. Convert the mass [tex]\(m\)[/tex] from kilograms to grams:
[tex]\[ m = 0.465 \text{ kg} \times 1000 \frac{\text{g}}{\text{kg}} = 465 \text{ g} \][/tex]

4. Rearrange the specific heat formula to solve for [tex]\( C_p \)[/tex]:
[tex]\[ C_p = \frac{q}{m \cdot \Delta T} \][/tex]

5. Substitute the known values into the equation:
[tex]\[ C_p = \frac{3000.0 \text{ J}}{465 \text{ g} \times 50.0^\circ\text{C}} \][/tex]

6. Calculate the specific heat [tex]\( C_p \)[/tex]:
[tex]\[ C_p = \frac{3000.0}{465 \times 50.0} \][/tex]
[tex]\[ C_p = \frac{3000.0}{23250} \][/tex]
[tex]\[ C_p \approx 0.129 \text{ J/g}^\circ\text{C} \][/tex]

Therefore, the specific heat of the substance is approximately [tex]\(0.129 \text{ J/g}^\circ\text{C}\)[/tex].

Among the given options:
- [tex]\(0.00775 \text{ J/g}^\circ\text{C}\)[/tex]
- [tex]\(0.0600 \text{ J/g}^\circ\text{C}\)[/tex]
- [tex]\(0.129 \text{ J/g}^\circ\text{C}\)[/tex]
- [tex]\(0.155 \text{ J/g}^\circ\text{C}\)[/tex]

The correct answer is [tex]\( 0.129 \text{ J/g}^\circ\text{C} \)[/tex].
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