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Heat Transfer and Phase Change

A block of ice at $-10^{\circ} \mathrm{C}$ and mass $\mathrm{ 0.5 \mathrm{~kg}}$ is heated until it becomes stcam at $\mathrm{ 100^{\circ} \mathrm{C}}$ Calculate the total heat energy required for this process, considering the different phases. Given: Specific heat of ice $\mathrm{ c_{i c e}=2.09 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}}$ , specific heat of water $\mathrm{ c_{\text {water }}=4.18 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}}$ , latent heat of fusion of ice $\mathrm{L_f=334 \mathrm{~J} / \mathrm{g}}$ , and latent heat of vaporization of water $\mathrm{L_v=2260 \mathrm{~J} / \mathrm{g}.}$

Option: 1
$1516.45 \mathrm{KJ}$

Option: 2
$185.02 \mathrm{KJ}$

Option: 3
$1225.2 \mathrm{KJ}$

Option: 4
$2320.02 \mathrm{KJ}$

Answers (1)

best_answer

The total heat energy is the sum of heat absorbed during phase changes and heat required to change the temperature.

For ice to $0^{\circ} \mathrm{C} :$

$\mathrm{ Q_{1}=m \cdot c_{\text {ice }} \cdot \Delta T }$

$\mathrm{ Q_1=0.5 \mathrm{~kg} \cdot 2.09 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C} \cdot(0 C-(-10 C)) }$

$\mathrm{ Q_1=10.45 \mathrm{~kJ}}$

During melting (ice to water):

$\mathrm{ Q_2=m \cdot L_f }$

$\mathrm{ Q_2=0.5 \mathrm{~kg} \cdot 334 \mathrm{~J} / \mathrm{g} }$

$\mathrm{ Q_2=167 \mathrm{~kJ}}$

For water to $\mathrm{100^{\circ} \mathrm{C} :}$

$\mathrm{ Q_3=m \cdot c_{\text {water }} \cdot \Delta T }$

$\mathrm{ Q_3=0.5 \mathrm{~kg} \cdot 4.18 \mathrm{~J} / \mathrm{g}^0 \mathrm{C} \cdot(100 C-0 C) }$

$\mathrm{ Q_3=209 \mathrm{kJ}}$

During vaporization (water to steam):

$\mathrm{ Q_4=m \cdot L_v }$

$\mathrm{ Q_4=0.5 \mathrm{~kg} \cdot 2260 \mathrm{~J} / \mathrm{g} }$

$\mathrm{ Q_4=1130 \mathrm{~kJ} }$

Total heat energy:

$\mathrm{ Q_{\text {total }}=Q_1+Q_2+Q_3+Q_4 }$

$\mathrm{ Q_{\text {total }}=10.45 \mathrm{~kJ}+167 \mathrm{~kJ}+209 \mathrm{~kJ}+1130 \mathrm{~kJ} }$

$\mathrm{ Q_{\text {total }}=1516.45 \mathrm{~kJ}}$

Therefore, the correct option is 1

Posted by

Kuldeep Maurya

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