When 1.0 tablespoon of butter is burned or used by our body, it r...

Question

When 1.0 tablespoon of butter is burned or used by our body, it releases 100 kcal (100 food Calories or 418. 4 kJ) of energy. If we could use all the energy provided, how many tablespoons of butter would have to be burned to raise the temperature of 3.00 L of water from 18.0 ℃ to 90.0 ℃

Accepted Answer

Welcome back, everyone. Burning one tablespoon of glucose can provide 90 kg of energy. Assuming that all of the energy from glucose can be used up determined. The number of tablespoons of glucose needed to be burned to increase the temperature of 2.5 liters of water. Initially at 27 degrees Celsius to 85 degrees Celsius. Let's begin by recalling our specific heat equation or specific heat formula where Q for heat is related or set equal to the mass of our substance, which is then multiplied by its specific heat capacity C which is then multiplied by the difference in temperature. Delta T. Now the substance that we are increasing the temperature of which is going to be water as mentioned in the prompt. And we're going to begin by determining the amount of heat that is required to raise the temperature of water. And so we're going to say that we're solving for the Q or heat of water, which is found by taking the mass of water, which in this case is based on 2.50 liters, which we should multiply to convert from liters in the denominator to milliliters in the numerator and then multiply to go from milliliters in the denominator to then grams so that we have mass of water. So beginning that conversion, we're going to recall that our prefix Millie tells us that we have an equivalent of 10 to the negative third leaders in the denominator canceling out leaders. We then will convert from milliliters to grams of water by utilizing our density of water, which we should recall is that we have one g per mil liter. And so we can then cancel out and let's just rewrite this. We can cancel out our units of milliliters. And now we have mass of water. Now we will then multiply by the specific heat capacity of water, which from our textbooks, we should recall is the value of one point oh calories per gram times degrees Celsius. And then we will multiply by the difference in temperature. Delta T where we would plug in the higher temperature or final temperature of 85 degrees Celsius subtracted by the initial temperature of 27 degrees Celsius. And that is our delta T final minus initial temperature. So, simplifying in our next line, we should have the mass term B 2500 g of water, which is multiplied by one calorie per gram times degrees Celsius. And then we've got multiplied by that, the result of Delta T, which is 58 degrees Celsius. And we can then focus on canceling out our units of Celsius as long along with grams. And that leaves us with calories where we should recall that the unit for heat is going to be in kilocalories. So in our next line, we're going to simplify so that we get a heat equal to 1.45 times 10 to the fifth power calories. And we will multiply to go from calories in the denominator to kilocalories in the numerator where our prefix kilo tells us that we have an equivalent of 10 to third calories in the denominator. So canceling out calories, we are left with kilocalories for their unit of heat. And we will find a total of kilocalories of heat that is required to raise the temperature of water to 85 degrees Celsius. And now we need to figure out the number of tablespoons of glucose needed to be burned in order to get to that heat required. And so the number of tablespoons of glucose C six H 12 06 required, we will determine by taking the total heat needed, which we stated is 145 kilocalories from our calculation above. And we will multiply by the amount of energy one tablespoon of glucose burnt can provide which from the prompt we're told is kilocalories for one tablespoon of glucose that is burnt. And so canceling out kilocalories, we're left with tablespoons of glucose as our final unit. And this will result in a value of 1. tablespoons of glucose required. And so this amount of glucose, 1.6 tablespoons is our final answer to complete this example as the amount required in order to be burned, to raise the temperature of the water to 85 degrees Celsius. I hope that this made sense and let us know if you have any questions.

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When 1.0 tablespoon of butter is burned or used by our body, it releases 100 kcal (100 food Calories or 418. 4 kJ) of energy. If we could use all the energy provided, how many tablespoons of butter would have to be burned to raise the temperature of 3.00 L of water from 18.0 ℃ to 90.0 ℃

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