In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 kg of water. (b) How much time is required? Assume that all of the heater's power goes into heating the water

Video transcript

Welcome back everybody. We are taking a look at an electric kettle and we are told that If we use an electric kettle that uses 2200 watts Uh we can use it to heat a mass of 1.8 kg of water from a temperature of 25°C. All the way up to 90°C. And we are tasked with finding how long it will take for this electric kettle to make the water boil. Well, I'm looking at all these terms here and it looks like we're gonna have to use this formula here that are heat is equal to our mass times our specific heat of water times our chains and temperature. Just as a side note here, the specific heat of water, it's 4180 jewels per kilogram Celsius. Now here's the thing though, we don't necessarily know how much heat is transferred, but we can equate this to another value. We can equate our cue two E, which is equal to energy transformed. Now the formula for energy transformed is simply power times our time that we are looking for, meaning that if we combine these two equations right here, we get that power times, time is equal to our mass times our specific heat times our change in temperature. Now, in order to isolate our time term, going to divide both sides by power and we get that our time is equal to M C delta T. Overpay. So now that we have our formula, let's go ahead and plug in our values to find how long it takes. So we have our mass of 1.8 kg. This is times our specific heat of water to be 4180 jewels per kilogram Celsius. Then we have, our change in temperature is just the final temperature of 90 minus our initial temperature of 25. And we divide all of this by how much power the electric kettle is using, which is 22 200 watts. When you plug this all into our calculator, we get 222.3 seconds but it looks like we need our answer in minutes. So per one minute there is 60 seconds. These units will cancel out. And we get that the time it takes for the water to boil with the electric kettle is 3.71 minutes corresponding to our answer choice of B. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.