Question

Your roommate leaves a 120W fan running in your apartment.Over the course of an hour,how much thermal energy does the fan add to the air ?

Answer 1

The fan adds 4.32 × 10⁵ J ( = 0.12 kWh ) of thermal energy to the air

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Further explanation

Let's recall the Power formula:

$\boxed {P = E \div t }$

$\boxed {E = P \times t }$

where :

E = energy ( J )

P = power ( W )

t = time taken ( s )

Let us now tackle the problem!

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Given:

power of fan = P = 120 W = 0.12 kW

time taken = t = 1 hour

Asked:

thermal energy = E = ?

Solution:

We will calculate the thermal energy as follows:

$P = E \div t$

$E = P \times t$

$E = 0.12 \times 1$

$\boxed {E = 0.12 \texttt{ kWh}}$

$E = 0.12 \times 3.6 \times 10^6 \texttt{ J}$ → 1 kWh = 3.6 × 10⁶ J

$\boxed {E = 4.32 \times 10^5 \texttt{ J}}$

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Conclusion:

The fan adds 4.32 × 10⁵ J ( = 0.12 kWh ) of thermal energy to the air

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Energy

Answer 2

Answer:

$4.32\cdot 10^5 J$

Explanation:

Power is related to energy by the following relationship:

$P=\frac{E}{t}$

where

P is the power used

E is the energy used

t is the time elapsed

In this problem, we know that

- the power of the fan is P = 120 W

- the fan has been running for one hour, which corresponds to a time of

$t = 1 h \cdot (60 min/h)(60 s/min)=3600 s$

So we can re-arrange the previous equation to find E, the energy (in the form of thermal energy) released by the fan:

$E=Pt=(120 W)(3600 s)=4.32\cdot 10^5 J$