Chapter U5, Problem 8STP

Interpretation Introduction

Interpretation:

The energy needed to raise the temperature of 32 g of ice from - 4.0 °C to 24°C needs to be determined,if specific heat capacity of ice is 0.49 cal/g°C and heat of fusion of water is 79.9 cal/g°C.

Concept introduction:

Due to transfer of energy the temperature of any substance increases or decreases. The change in temperature for the addition of energy can be calculated with the help of calorimetric equation:

$\begin{array}{l}\text{Q = m × C × ΔT}\\ \text{Here:}\\ \text{Q}\text{}\text{ = heat change }\\ \text{m = mass}\\ \text{C = specific heat }\\ \text{ΔT = change in T}\end{array}$

Answer to Problem 8STP

Option (D) is correct.

Explanation of Solution

Mass of ice = 32 g

Initial temperature = - 4.0 °C

Final temperature = 24°C

Melting point of ice = 0°C

Specific heat capacity of ice 0.49 cal/g°C

Heat of fusion of water = 79.9 cal/g°C

Step-1:

Heat change from- 4.0 °C to 0°C

$\begin{array}{l}\text{q = m × C × ΔT}\\ \text{q = 32 g × 0}\text{.49 cal/g°C × (0-(-4°C )}\\ \text{q = 62}\text{.7cal}\end{array}$

Step-2:

Melting of ice at 0°C

$\begin{array}{l}\text{q = 79}\text{.9cal/g°C×32g}\\ \text{q = 2557cal}\end{array}$

Step-3:

Heat change from 0°C to 24°C

$\begin{array}{l}\text{q = m × C × ΔT}\\ \text{q = 32 g × 1 cal/g°C × (24-0°C )}\\ \text{q = 768 cal}\end{array}$

Total heat change = $\text{62}\text{.7 + 2557 + 768 = 3388 = 3400 cal}$

Conclusion

Reasons for incorrect options:

Total heat change during the melting of ice from 0°C to 24 °C must be sum of all the three steps of process:

• Change in temperature from -4 °C to 0 °C
• Fusion of ice at 0°C
• Change in temperature from 0°C to 24°C