# Is my textbook incorrect?

They have us two containers, one which has more water in it and other has less water. They are heated at the same temperature. Which one will have higher heat?

My book is saying the one with little water in it will have more heat. But how?

"If a large mass is at_ a higher temperature it will have more heat energy than a smaller mass at that temperature." So why isn't this the case here?

Isn't heat directly proportional to mass? The larger the mass the more heat in it?

• "They are heated at the same temperature. Which one will have a higher temperature?"...is this a trick question or did something get lost in translation here? It sounds as if you're asking "if I heat two things to the same temperature, which one will have the higher temperature", which is non-sensical - if they have different temperatures you didn't "heat them to the same temperature". – ACuriousMind Feb 12 '17 at 16:25
• No, I guess it is like that, because it is meant to say, because objects mass will make it either higher or smaller but I am not sure why my teacher is saying lower water container will have more heat temperature. youtube.com/watch?v=-mMt4DGFjp0 – Okama Ksakas Feb 12 '17 at 16:27
• You're using temperature instead of heat it seems like. If they are heated by something the same temperature, the one will less volume should heat up quicker because there is less mass to heat up. I'm not sure what you mean by "I saw a video stating that the higher the mass the higher the temperature will be of that object, so why isn't this the case?". If a large mass is at a higher temperature it will have more heat energy than a smaller mass at that temperature. – JMac Feb 12 '17 at 16:27
• "If a large mass is at_ a higher temperature it will have more heat energy than a smaller mass at that temperature.". Yep, that's what I am exactly trying to say, but my teacher is saying the reverse, as in the small water container will include more heat. – Okama Ksakas Feb 12 '17 at 16:29
• OP has been modified and I hope it makes sense now. – Okama Ksakas Feb 12 '17 at 16:30

## 1 Answer

The formula $Q=mc\Delta T$ tells us how much energy is required to heat up a mass of any substance, with $m$ being the mass of the substance, $c$ being the specific heat and $\Delta T$ being the change in temperature. Given that the same substance is being heated at the same temperature for the same time period but for different masses, we can equate $Q$ to get:
$m_1c\Delta T_1=m_2c\Delta T_2$, where $m_1>m_2$
We can cut out the $c$ because we're heating the same substance to get:
$m_1\Delta T_1=m_2\Delta T_2$
From this we know that if $m_1>m_2$ then $\Delta T_2>\Delta T_1$
Therefore the rise in temperature of the smaller quantity of water is greater.