Question

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)

Answer 1

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:

`mc\Delta T=mgh`

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:

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

Now, plug in the values and solve for ΔT:

`\begin{gathered} \Delta T=(gh)/(c) \\ \\ \Delta T=(9.8*15.0)/(0.20*10^3*4.2) \\ \\ \Delta T=(147)/(840) \\ \\ \Delta T=0.175^o\text{ C} \end{gathered}`

Therefore, the temperature change is 0.175° C.

• ANSWER:

0.175° C