QuestionHow much mass of aluminum fins, in grams, is needed to heat from $14.25^{\circ} \mathrm{C}$ to $23.05^{\circ} \mathrm{C}$ using $2101 \mathrm{~J}$ ? Specific heat is $0.897 \mathrm{~J/(g \cdot {}^{\circ}C)}$ .

Studdy Solution

STEP 1

Assumptions1. The energy absorbed by the aluminum fins is2101 J. The initial temperature of the aluminum fins is14.25 °C3. The final temperature of the aluminum fins is23.05 °C4. The specific heat of aluminum is0.897 J/(g°C)
5. The heat absorbed or released by a substance is given by the formula $q = mc\Delta$ where - q is the heat absorbed or released, - m is the mass of the substance, - c is the specific heat of the substance, and - Δ is the change in temperature.

STEP 2

First, we need to calculate the change in temperature. We can do this by subtracting the initial temperature from the final temperature.
$\Delta =_{final} -_{initial}$

STEP 3

Now, plug in the given values for the initial and final temperatures to calculate the change in temperature.
$\Delta =23.05^{\circ}C -14.25^{\circ}C$

STEP 4

Calculate the change in temperature.
$\Delta =23.05^{\circ}C -14.25^{\circ}C =8.8^{\circ}C$

STEP 5

Now that we have the change in temperature, we can rearrange the heat equation to solve for the mass of the aluminum fins. The rearranged equation is $m = \frac{q}{c\Delta}$

STEP 6

Plug in the values for the heat absorbed, the specific heat of aluminum, and the change in temperature to calculate the mass.
$m = \frac{2101 J}{0.897 J/(g°C) \times8.8°C}$

STEP 7

Calculate the mass of the aluminum fins.
$m = \frac{2101 J}{0.897 J/(g°C) \times.°C} =268.5 g$ The mass of the aluminum fins that could be heated from14.25 °C to23.05 °C by2101 J of energy is268.5 g.

Was this helpful?

QuestionHow much mass of aluminum fins, in grams, is needed to heat from $14.25^{\circ} \mathrm{C}$ to $23.05^{\circ} \mathrm{C}$ using $2101 \mathrm{~J}$ ? Specific heat is $0.897 \mathrm{~J/(g \cdot {}^{\circ}C)}$ .

Studdy Solution

STEP 1

STEP 2

First, we need to calculate the change in temperature. We can do this by subtracting the initial temperature from the final temperature.
$\Delta =_{final} -_{initial}$

STEP 3

Now, plug in the given values for the initial and final temperatures to calculate the change in temperature.
$\Delta =23.05^{\circ}C -14.25^{\circ}C$

STEP 4

Calculate the change in temperature.
$\Delta =23.05^{\circ}C -14.25^{\circ}C =8.8^{\circ}C$

STEP 5

Now that we have the change in temperature, we can rearrange the heat equation to solve for the mass of the aluminum fins. The rearranged equation is $m = \frac{q}{c\Delta}$

STEP 6

Plug in the values for the heat absorbed, the specific heat of aluminum, and the change in temperature to calculate the mass.
$m = \frac{2101 J}{0.897 J/(g°C) \times8.8°C}$

STEP 7

Calculate the mass of the aluminum fins.
$m = \frac{2101 J}{0.897 J/(g°C) \times.°C} =268.5 g$ The mass of the aluminum fins that could be heated from14.25 °C to23.05 °C by2101 J of energy is268.5 g.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionHow much mass of aluminum fins, in grams, is needed to heat from 14.25∘C14.25^{\circ} \mathrm{C}14.25∘C to 23.05∘C23.05^{\circ} \mathrm{C}23.05∘C using 2101 J2101 \mathrm{~J}2101 J? Specific heat is 0.897 J/(g⋅∘C)0.897 \mathrm{~J/(g \cdot {}^{\circ}C)}0.897 J/(g⋅∘C).

Studdy Solution

STEP 1

STEP 2

First, we need to calculate the change in temperature. We can do this by subtracting the initial temperature from the final temperature.Δ=final−initial\Delta =_{final} -_{initial}Δ=final​−initial​

STEP 3

Now, plug in the given values for the initial and final temperatures to calculate the change in temperature.Δ=23.05∘C−14.25∘C\Delta =23.05^{\circ}C -14.25^{\circ}CΔ=23.05∘C−14.25∘C

STEP 4

Calculate the change in temperature.Δ=23.05∘C−14.25∘C=8.8∘C\Delta =23.05^{\circ}C -14.25^{\circ}C =8.8^{\circ}CΔ=23.05∘C−14.25∘C=8.8∘C

STEP 5

Now that we have the change in temperature, we can rearrange the heat equation to solve for the mass of the aluminum fins. The rearranged equation ism=qcΔm = \frac{q}{c\Delta}m=cΔq​

STEP 6

Plug in the values for the heat absorbed, the specific heat of aluminum, and the change in temperature to calculate the mass.m=2101J0.897J/(g°C)×8.8°Cm = \frac{2101 J}{0.897 J/(g°C) \times8.8°C}m=0.897J/(g°C)×8.8°C2101J​

STEP 7

Calculate the mass of the aluminum fins.m=2101J0.897J/(g°C)×.°C=268.5gm = \frac{2101 J}{0.897 J/(g°C) \times.°C} =268.5 gm=0.897J/(g°C)×.°C2101J​=268.5gThe mass of the aluminum fins that could be heated from14.25 °C to23.05 °C by2101 J of energy is268.5 g.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionHow much mass of aluminum fins, in grams, is needed to heat from $14.25^{\circ} \mathrm{C}$ to $23.05^{\circ} \mathrm{C}$ using $2101 \mathrm{~J}$ ? Specific heat is $0.897 \mathrm{~J/(g \cdot {}^{\circ}C)}$ .

First, we need to calculate the change in temperature. We can do this by subtracting the initial temperature from the final temperature.
$\Delta =_{final} -_{initial}$

Now, plug in the given values for the initial and final temperatures to calculate the change in temperature.
$\Delta =23.05^{\circ}C -14.25^{\circ}C$

Calculate the change in temperature.
$\Delta =23.05^{\circ}C -14.25^{\circ}C =8.8^{\circ}C$

Now that we have the change in temperature, we can rearrange the heat equation to solve for the mass of the aluminum fins. The rearranged equation is $m = \frac{q}{c\Delta}$

Plug in the values for the heat absorbed, the specific heat of aluminum, and the change in temperature to calculate the mass.
$m = \frac{2101 J}{0.897 J/(g°C) \times8.8°C}$

Calculate the mass of the aluminum fins.
$m = \frac{2101 J}{0.897 J/(g°C) \times.°C} =268.5 g$ The mass of the aluminum fins that could be heated from14.25 °C to23.05 °C by2101 J of energy is268.5 g.