Question Video: Combined Variation and Its Applications | Nagwa Question Video: Combined Variation and Its Applications | Nagwa

# Question Video: Combined Variation and Its Applications

When a given substance is heated, the change in its temperature varies directly with the amount of energy transferred to the substance, and it varies inversely with the mass of the substance. Write an equation for the change in temperature ฮ๐ in terms of the amount of energy transferred ๐ธ and the mass ๐. The temperature of 25 g of olive oil increases by 11.5ยฐ C when it receives 575 J of energy. Find the temperature increase of 115 g of olive oil when it receives 460 J of energy.

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### Video Transcript

When a given substance is heated, the change in its temperature varies directly with the amount of energy transferred to the substance, and it varies inversely with the mass of the substance. Write an equation for the change in temperature ฮ๐ in terms of the amount of energy transferred ๐ธ and the mass ๐. And the second part of question says, the temperature of 25 grams of olive oil increases by 11.5 degrees Celsius when it receives 575 joules of energy. Find the temperature increase of 115 grams of olive oil when it receives 460 joules of energy.

Well, if we take a look at the information weโve been given in the question, first of all, we know that if a substance is heated, the change in its temperature varies directly with the amount of energy. So therefore, what we can say is that temperature change is directly proportional to ๐ธ because ๐ธ is the energy transferred. And then, what weโre also told is that it varies inversely with the mass of the substance. So therefore, what we can say is that the temperature change is proportional to one over ๐ or the temperature change is inversely proportional to ๐.

So now, what we want to do is write an equation. And to do that, what weโre gonna do is introduce ๐, our proportionality constant. So, weโre gonna have the change in temperature is equal to ๐, our proportionality constant, multiplied by ๐ธ. And thatโs because we know that the energy transferred is directly proportional to the change in temperature. And then, this is all over ๐ because the change in temperature was inversely proportional to the mass. So, our equation is-is ฮ๐, so the change in temperature, is equal to ๐๐ธ over ๐.

Okay, so now what we can do is use this to help us solve the second part of the question. But what we want to do with any question like this, so involving proportionality, is find out what ๐ is. So, we need to find our proportionality constant. So, if we check out the second part, we know straight away the change in temperature is 11.5. And this is when the energy is 575 joules and the mass of olive oil is 25 grams. Well, now, what we can do is substitute these values into the equation we got in part one.

And when we do that, what weโre gonna get is 11.5 equals 575๐ over 25, remembering that what weโre looking to do here is find the proportionality constant because that will help us to solve the problem. So, what weโre gonna do next is multiply through by 25. So, when weโve done this, what we get is 287.5 equals 575๐. So then, we can divide through by 575, which gives us a value of ๐ of 0.5. So great, weโve now found our proportionality constant.

So, if we substitute this back into the original equation, what we get is ฮ๐ is equal to 0.5๐ธ over ๐. So now, what we want to do is use this to find the temperature increase of 115 grams of olive oil when it receives 460 joules of energy. So now, we donโt know the change in temperature cause this is what weโre looking for.

We know the energy transferred, which is 460 joules. And we also know the mass, which is 115. So therefore, we can say that ฮ๐, our change in temperature, is gonna be equal to 0.5 multiplied by 460 over 115, which is gonna be equal to 230 over 115. So therefore, we can say that the temperature increase of 115 grams of olive oil when it receives 460 joules of energy is two degrees Celsius.

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