Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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

Sagot :

Given:

The mass of ice is m = 50 g

The initial temperature of ice is

[tex]T_i=\text{ 0 }^{\circ}\text{ C}[/tex]

The final temperature of the water is

[tex]T_f=\text{ 35}^{\circ}C[/tex]

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

[tex]Q_1\text{ = mL}_f[/tex]

Here, the latent heat of fusion is

[tex]L_f=\text{ 80 cal/g}[/tex]

On substituting the values, the heat will be

[tex]\begin{gathered} Q_1=50\text{ }g\text{ }\times80\text{ cal/g} \\ =4000\text{ cal} \end{gathered}[/tex]

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

[tex]\begin{gathered} Q_2=mc(\Delta\text{ T}) \\ =mc(T_f-T_i) \end{gathered}[/tex]

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

[tex]\begin{gathered} Q_2=50\text{ g}\times1\text{ cal/g }^{\circ}C\times(35-0) \\ =\text{ 1750 cal} \end{gathered}[/tex]

The total heat will be

[tex]\begin{gathered} Q=Q_1+Q_2 \\ =4000+1750 \\ =5750\text{ cal} \end{gathered}[/tex]

Final Answer:

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