# Find the amount of heat energy needed to convert 150 grams of ice at -15°C to ice at -63°C?

## Find the amount of heat energy needed to convert 150 grams of ice at -15°C to ice at -63°C. Choices: a. 14760 Joules because the ice is cooling. b. (-) 14760 Joules because the ice is cooling. c. (-) 14760 Joules because the ice is being heated. d. 14760 Joules because the ice is being heated.

May 4, 2017

I'd have to go with (b).

#### Explanation:

The problem with this question is that you can't really have negative heat, but you can have negative enthalpy change, $\Delta H$.

We always look at things from the perspective of the system. When the system, which in your case is the sample of ice, is gaining heat, we say that it undergoes a positive enthalpy change

$\Delta H > 0 \to$ the system gained heat

When the system is losing heat, we say that it undergoes a negative enthalpy change

$\Delta H < 0 \to$ the system lost heat

In other words, we use a minus sign to describe heat lost.

In both cases, the heat itself is positive, but the sign that it carries tells you if it is being gained or lost.

In this example

$\Delta H = + \text{14760 J} \to$ the ice absorbed $\text{14760 J}$ of heat

$\Delta H = - \text{14760 J} \to$ the ice gave off $\text{14760 J}$ of heat

In the first case, energy entered the system, hence the $+$ sign. In the second case, energy left the system, hence the $-$ sign.

In order for your sample of ice to go from $- {15}^{\circ} \text{C}$ to $- {63}^{\circ} \text{C}$, it must give off heat. So you don't need heat to decrease the temperature of the ice.

Right from the start, you can say that options (c) and (d) make no sense because you cannot decrease the temperature of the ice by heating it.

Now, the only valid option is

(b) $- \text{14760 J}$ because the ice is cooling

but a more accurate description would be

(b) $\Delta H = - \text{14760 J}$ because the ice is cooling

The enthalpy change carries a negative sign because the heat is being lost. How much heat is being lost? $\text{14760 J}$.