Question

How much heat is necessary to change 295 g of ice at -5°C to water at 20°C? Answer must be in kcal

Answer 1

Given:

• Mass of ice = 295 g ==> 0.295 kg

,

• Initial temperature, T1 = -5°C

,

• Final temperature, T2 = 20°C

Let's find the amount of heat necessary to change the ice to water.

To find the amount of heat, let's apply the Specific Heat Capacity formula:

`\begin{gathered} Q=mc\Delta T \\ \\ Q=mc(T_2-T_1) \end{gathered}`

Where:

m is the mass in kg = 0.295 kg

T1 is the initial temperature

T2 is the final temperature.

c is the specific heat capacity

Let's first find the amount of heat required to change ice from -5°C to 0°C.

`\begin{gathered} Q_1=0.295*0.50*(0-(-5)) \\ \\ Q_1=0.295*0.50*5 \\ \\ Q_1=0.74\text{ kcal} \end{gathered}`

Now, let's find the heat required to change from 0°C(ice) to 0°C(water).

We have:

`\begin{gathered} Q_2=m*L \\ \end{gathered}`

Where L is the latent fusion of water:

`\begin{gathered} Q_2=0.295*79.7 \\ \\ Q_2=23.51\text{ kcal} \end{gathered}`

Now, let's find the heat required to change 0°C (water) to 20°C(water).

We have:

`\begin{gathered} Q_3=mc_(water)(T_2-T_1) \\ \\ Q_3=0.295*1.0*(20-0) \\ \\ Q_3=0.295*1.0*20 \\ \\ Q_3=5.9\text{ kcal} \end{gathered}`

Therefore, the total heat required is:

Q = Q1 + Q2 + Q3

Thus, we have:

`\begin{gathered} Q=0.74+23.51+5.9 \\ \\ Q=30.15\text{ kcal} \end{gathered}`

Therefore, the amount of heat neccesary is