lilbre948
contestada

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 ?

Respuesta :

Answer:

[tex]4.32\cdot 10^5 J[/tex]

Explanation:

Power is related to energy by the following relationship:

[tex]P=\frac{E}{t}[/tex]

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

[tex]t = 1 h \cdot (60 min/h)(60 s/min)=3600 s[/tex]

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

[tex]E=Pt=(120 W)(3600 s)=4.32\cdot 10^5 J[/tex]

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

[tex]\texttt{ }[/tex]

Further explanation

Let's recall the Power formula:

[tex]\boxed {P = E \div t }[/tex]

[tex]\boxed {E = P \times t }[/tex]

where :

E = energy ( J )

P = power ( W )

t = time taken ( s )

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

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:

[tex]P = E \div t[/tex]

[tex]E = P \times t[/tex]

[tex]E = 0.12 \times 1[/tex]

[tex]\boxed {E = 0.12 \texttt{ kWh}}[/tex]

[tex]E = 0.12 \times 3.6 \times 10^6 \texttt{ J}[/tex] → 1 kWh = 3.6 × 10⁶ J

[tex]\boxed {E = 4.32 \times 10^5 \texttt{ J}}[/tex]

[tex]\texttt{ }[/tex]

Conclusion:

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

[tex]\texttt{ }[/tex]

Learn more

  • Velocity of Runner : https://brainly.com/question/3813437
  • Kinetic Energy : https://brainly.com/question/692781
  • Acceleration : https://brainly.com/question/2283922
  • The Speed of Car : https://brainly.com/question/568302

[tex]\texttt{ }[/tex]

Answer details

Grade: High School

Subject: Mathematics

Chapter: Energy

Ver imagen johanrusli