Question

How many calories are needed to melt 50 grams of ice at 0°C and convert it to liquid water at 35°C?

Answer 1

Given:

The mass of ice is m = 50 g

The initial temperature of ice is

`T_i=\text{ 0 }^(\circ)\text{ C}`

The final temperature of the water is

`T_f=\text{ 35}^(\circ)C`

Step-by-step explanation:

Heat is first required to convert ice to water at 0 degrees Celsius.

The heat required to convert ice to water at 0 degrees Celsius can be calculated by the formula

`Q_1\text{ = mL}_f`

Here, the latent heat of fusion is

`L_f=\text{ 80 cal/g}`

On substituting the values, the heat will be

`\begin{gathered} Q_1=50\text{ }g\text{ }*80\text{ cal/g} \\ =4000\text{ cal} \end{gathered}`

Now, the heat required to increase the temperature of water from 0 degrees Celsius to 35 degrees Celsius can be calculated by the formula

`\begin{gathered} Q_2=mc(\Delta\text{ T}) \\ =mc(T_f-T_i) \end{gathered}`

Here, c is the specific heat of water at 1 cal/g deg C

On substituting the values, the heat required to increase the temperature will be

`\begin{gathered} Q_2=50\text{ g}*1\text{ cal/g }^(\circ)C*(35-0) \\ =\text{ 1750 cal} \end{gathered}`

The total heat will be

`\begin{gathered} Q=Q_1+Q_2 \\ =4000+1750 \\ =5750\text{ cal} \end{gathered}`

Final Answer:

The heat required to convert 50 grams of ice to water from 0 degrees Celsius to 35 degrees Celsius is 5750 cal