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A 200 \mathrm{~g} sample of ice at -15^{\circ} \mathrm{C}  is heated until it completely vaporizes into steam at 120^{\circ} \mathrm{C}.Calculate the total heat transfer during this process, including the heat required for fusion and vaporization. Additionally, determine the change in entropy during each phase transition and the total change in entropy for the entire process. Given the specific heat capacity of ice is 2.09 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right), the specific heat capacity of water is 4.18 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right), the heat of fusion of ice is 334 \mathrm{~J} / \mathrm{g},  the heat of vaporization of water is 2260 \mathrm{~J} / \mathrm{g}, and the molar gas constant is 8.314 \mathrm{~J} /(\mathrm{mol} \mathrm{K}).

Option: 1

1455.19 \mathrm{~J} / \mathrm{K}


Option: 2

1455.19 \mathrm{~J} / \mathrm{K}


Option: 3

1455.19 \mathrm{~J} / \mathrm{K}


Option: 4

1455.19 \mathrm{~J} / \mathrm{K}


Answers (1)

Step 1: Calculate the heat required to raise the temperature of the ice to its melting point \left(0^{\circ} \mathrm{C}\right) :
\mathrm{Q_{\text {ice }}=m_{\text {ice }} \cdot c_{\text {ice }} \cdot \Delta T}

Where: \mathrm{-m_{\text {ice }} \text{is the mass of the ice} -c_{\text {ice }} \text{is the specific heat capacity of ice} - \Delta T}is the temperature change

Substitute the given values:
\begin{gathered} Q_{\text {ice }}=200 \mathrm{~g} \cdot 2.09 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right) \cdot\left(0{ }^{\circ} \mathrm{C}-\left(-15^{\circ} \mathrm{C}\right)\right) \\ Q_{\text {ice }}=6270 \mathrm{~J} \end{gathered}

Step 2: Calculate the heat required for the fusion of ice at its melting point \left(0^{\circ} \mathrm{C}\right) :
Q_{\text {fusion }}=m_{\text {ice }} \cdot \Delta H_{\text {fusion }}

Where: -\Delta H_{\text {fusion }} is the heat of fusion of ice

Substitute the given value:
\begin{gathered} Q_{\text {fusion }}=200 \mathrm{~g} \cdot 334 \mathrm{~J} / \mathrm{g} \\ Q_{\text {fusion }}=66800 \mathrm{~J} \end{gathered}

Step 3: Calculate the heat required to raise the temperature of the water from its melting point \left(0^{\circ} \mathrm{C}\right) to its boiling point  \left(100^{\circ} \mathrm{C}\right) :
Q_{\text {water }}=m_{\text {water }} \cdot c_{\text {water }} \cdot \Delta T
Where: -m_{\text {water }} is the mass of the water -c_{\text {water }} is the specific heat capacity of water

Substitute the given values:
\begin{gathered} Q_{\text {water }}=200 \mathrm{~g} \cdot 4.18 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right) \cdot\left(100^{\circ} \mathrm{C}-0{ }^{\circ} \mathrm{C}\right) \\ Q_{\text {water }}=83600 \mathrm{~J} \end{gathered}

Step 4: Calculate the heat required for the vaporization of water at its boiling point \left(100^{\circ} \mathrm{C}\right):
Q_{\text {vaporization }}=m_{\text {water }} \cdot \Delta H_{\text {vaporization }}

Where: -\Delta H_{\text {vaporization }} is the heat of vaporization of water Substitute the given value:
\begin{gathered} Q_{\text {vaporization }}=200 \mathrm{~g} \cdot 2260 \mathrm{~J} / \mathrm{g} \\ Q_{\text {vaporization }}=452000 \mathrm{~J} \end{gathered}

Step 5: Calculate the total heat transfer during the entire process:
\mathrm{Q_{\text {total }}=Q_{\text {ice }}+Q_{\text {fusion }}+Q_{\text {water }}+Q_{\text {vaporization }}}
Substitute the calculated values:
\begin{gathered} Q_{\text {total }}=6270 \mathrm{~J}+66800 \mathrm{~J}+83600 \mathrm{~J}+452000 \mathrm{~J} \\ Q_{\text {total }}=605370 \mathrm{~J} \end{gathered}
 

Step 6: Calculate the change in entropy for each phase transition: Entropy change during fusion:
\Delta S_{\text {fusion }}=\frac{Q_{\text {fusion }}}{T_{\text {fusion }}}
Where: - T_{\text {fusion }} is the melting point of ice in Kelvin (273.15 \mathrm{~K}) Substitute the values:
\begin{gathered} \Delta S_{\text {fusion }}=\frac{66800 \mathrm{~J}}{273.15 \mathrm{~K}} \\ \Delta S_{\text {fusion }}=244.45 \mathrm{~J} / \mathrm{K} \end{gathered}

Entropy change during vaporization:
\Delta S_{\text {vaporization }}=\frac{Q_{\text {vaporization }}}{T_{\text {vaporization }}}
Where: - T_{\text {vaporization }}  is the boiling point of water in Kelvin (373.15 \mathrm{~K}) Substitute the values:
\begin{gathered} \Delta S_{\text {vaporization }}=\frac{452000 \mathrm{~J}}{373.15 \mathrm{~K}} \\ \Delta S_{\text {vaporization }}=1210.74 \mathrm{~J} / \mathrm{K} \end{gathered}

Step 7: Calculate the total change in entropy for the entire process:
\begin{gathered} \Delta S_{\text {total }}=\Delta S_{\text {fusion }}+\Delta S_{\text {vaporization }} \\ \Delta S_{\text {total }}=244.45 \mathrm{~J} / \mathrm{K}+1210.74 \mathrm{~J} / \mathrm{K} \\ \Delta S_{\text {total }}=1455.19 \mathrm{~J} / \mathrm{K} \end{gathered}

Answer: The total heat transfer during the process, including the heat required for fusion and vaporization, is 605370 \mathrm{~J}.The change in entropy during fusion is 244.45 \mathrm{~J} / \mathrm{K}, the change in entropy during vaporization is  1210.74 \mathrm{~J} / \mathrm{K}, and the total change in entropy for the entire process is 1455.19 \mathrm{~J} / \mathrm{K}.

 

Posted by

Ramraj Saini

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