EMF, Power Output, and Terminal Voltage

[phm]

Homework Statement

A battery supplies a steady current of 5.6 A for 21s. During this time 1410J of chemical energy is transformed into electric energy, but 560J of this electric energy is transformed into heat energy inside the battery.

a) What is the emf of the battery?

b) What is the total power output of the battery?

c) What is the terminal voltage fo the battery?

Homework Equations

emf= Ve + V
P= VI or P= V²/R
Ve= emf - V or Ve= emf- Ir

The Attempt at a Solution

My attempt to find the emf was (1410J)/(21s) and to multiply that by (1.6 X 10_-19), since the emf is the "amount of chemical energy transformed to electric potential energy per coulomb of charge." However, I am not sure if I am to include or minus the 560J from the 1410J.
Then to find the power output, I am assuming that you would use P=VI, where the V is the emf.
After that, I don't know how to find the terminal voltage.

 

[nickjer]

Looks like you just stuck the charge of a single electron in there. You know P=VI, and you know power is just a rate of energy, P = E/t. That means you have everything you need.

 

[nlightner]

I would like to clarify a few things before providing a response. EMF stands for electromotive force and is a measure of the potential difference between two points in an electrical circuit. It is often used interchangeably with the term "voltage." Power output refers to the rate at which energy is transferred or converted in a system, and terminal voltage refers to the potential difference between the positive and negative terminals of a battery or power source.

With that in mind, let's address the questions in the problem:

a) To find the emf of the battery, we can use the equation emf = ΔE/Δq, where ΔE is the change in energy and Δq is the change in charge. In this case, we are given the values for both ΔE (1410 J) and Δq (5.6 A for 21 s). Plugging these values into the equation, we get an emf of approximately 252 V.

b) The total power output of the battery can be found using the equation P = VI, where V is the emf and I is the current. Plugging in the values for V (252 V) and I (5.6 A), we get a power output of approximately 1411 W.

c) To find the terminal voltage of the battery, we can use the equation Ve = emf - IR, where Ve is the terminal voltage, emf is the electromotive force, I is the current, and R is the resistance. In this case, we are not given the value of resistance, so we cannot calculate the exact terminal voltage. However, we can use the values for emf (252 V) and I (5.6 A) to estimate the terminal voltage. Assuming a very small resistance (close to 0), the terminal voltage would be approximately equal to the emf, so the terminal voltage in this case would be approximately 252 V.

I hope this helps clarify the problem and how to approach it as a scientist. It is important to always use the correct equations and units when solving problems in science, and to carefully consider the given information before making calculations.