QuestionHeat of $8750 \mathrm{~J}$ raises aluminum's temp by $56.0^{\circ} \mathrm{C}$ . Specific heat is $900 \mathrm{~J} / \mathrm{Kg} \cdot{ }^{\circ} \mathrm{C}$ . Find mass.

Studdy Solution

STEP 1

Assumptions1. The amount of heat applied is $8750 \mathrm{~J}$ . The increase in temperature is $56.0^{\circ} \mathrm{C}$
3. The specific heat of aluminum is $900 \mathrm{~J} / \mathrm{Kg} \cdot{ }^{\circ} \mathrm{C}$
4. We are looking for the mass of the aluminum5. The heat transfer follows the formula $Q = mc\Delta$ , where $Q$ is the heat transferred, $m$ is the mass, $c$ is the specific heat, and $\Delta$ is the change in temperature

STEP 2

First, we need to rearrange the heat transfer formula to solve for the mass $m$ .
$m = \frac{Q}{c\Delta}$

STEP 3

Now, plug in the given values for the heat $Q$ , the specific heat $c$ , and the change in temperature $\Delta$ to calculate the mass.
$m = \frac{8750 \mathrm{~J}}{900 \mathrm{~J} / \mathrm{Kg} \cdot{ }^{\circ} \mathrm{C} \times56.0^{\circ} \mathrm{C}}$

STEP 4

Perform the multiplication in the denominator first.
$m = \frac{8750 \mathrm{~J}}{50400 \mathrm{~J} / \mathrm{Kg}}$

STEP 5

Finally, divide the numerator by the denominator to find the mass of the aluminum.
$m = \frac{8750 \mathrm{~J}}{50400 \mathrm{~J} / \mathrm{Kg}} =0.173 \mathrm{~Kg}$ The mass of the aluminum is0.173 Kg.

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