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A 25.0 kg bag of dirt falls 15.0 m at a construction site. Assuming that all of the heat produced is retained by the dirt, how much will its temperature increase? (cdirt = 0.20 cal/g•°C)

Respuesta :

Given:

• Mass of bag, m =25.0 kg

,

• Height, h = 15.0 m

,

• c = 0.20 cal/g•°C

Let's find by how much the temperature will increase.

Apply the Law of Conservation of Energy:

[tex]mc\Delta T=mgh[/tex]

Where:

• m is the mass

,

• c is the specific heat capacity

,

• g is acceleration due to gravity

,

• h is the height.

,

• ΔT is the temperature change.

Thus, we have:

[tex]\begin{gathered} mc\Delta T=mgh \\ \\ Eliminate\text{ m on both sides:} \\ c\Delta T=gh \end{gathered}[/tex]

Now, plug in the values and solve for ΔT:

[tex]\begin{gathered} \Delta T=\frac{gh}{c} \\ \\ \Delta T=\frac{9.8*15.0}{0.20\times10^3\times4.2} \\ \\ \Delta T=\frac{147}{840} \\ \\ \Delta T=0.175^o\text{ C} \end{gathered}[/tex]

Therefore, the temperature change is 0.175° C.

• ANSWER:

0.175° C

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