Problems based on latent heat of fusion and vaporization

Q: Latent heat of fusion of ice is:

Latent heat of fusion of ice\$=80 cal g^{-1}\$\$=80\times 4.2 J\times 10^3 kg^{-1}\$\$=336\times 10^3 J kg^{-1}\$

Q: For any substance, why does the temperature remain constant during the change of state?

Hint: The heat supplied to a system is used to break its intermolecular force of attraction.Explanation: The kinetic energy of particles in a substance is directly proportional to the temperature.The relation is shown as;\$K.E = \dfrac {3} {2}kT\$Where \$K.E\$ = Kinetic energy \$k\$ = Energy constant \$T\$ = Temperature As temperature increases the kinetic energy of particles also increases but in case of a change of state, the energy supplied to the substance by increasing temperature is used to break the intermolecular forces between the particles so that the state can be changed.Hence, the temperature remains constant as all the heat is used up and no external heat is released or absorbed.

Q: Calculate the mass of ice required to lower the temperature of \$300g\$ of water at \$40°C\$ to water at \$0°C\$. (Specific latent heat of ice = 336 J /g, Specific heat capacity of water = 4.2 J/ g°C).

Heat extracted by ice at \$0^oC\$ to melt = Heat given by water to reach \$0^oC\$ from \$40^oC\$.\$ML = mc\theta\$Where, \$\theta\$ = change in temperature of water L = Specific Latent heat of ice c = Specific heat capacity of water M = Mass of ice required m = mass of water\$M\times 336 =300\times 4.2\times (40-0)\$\$M=\dfrac{300\times 4.2\times 40}{336} = 150g\$\$\therefore\$ Ice required to lower the temperature of water \$= 150 g\$

Q: What is latent heat of fusion ?

Latent heat of fusion of a solid is defined as the amount of heat required to convert a unit mass of the substance from the solid state to the liquid state without changing the temperature.

Q: A piece of ice (heat capacity \$=2100Jkg^{-1}\$\$^oC^{-1}\$ and latent heat \$=3.36\times 10^{5}Jkg^{-1}\$) of mass \$m\$ grams is at \$-5^{o}C\$ at atmospheric pressure. It is given 420 \$J\$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

Heat \$=\$ latent heat \$+\$ Heat required to raise temp\$Q= mL + mC_{p} \Delta{T}\$\$420=(m\times 2100\times 5+1\times 3.36\times 10^{5})\times 10^{-3}\$ where \$m\$ is in gm.\$m=8 g\$

Q: The latent heat of vaporisation of water is:

The heat of fusion for water at 0 °C is approximately 334 joules (79.7 calories) per gram, and the heat of vaporization at 100 °C is about 2,250 joules (533 calories) per gram or \$2.25 *10^6\$ J/kg.

Q: A substance of mass m kg requires a power input of P watts to remain in the molten state at its melting point. When the power is turned off, the sample completely solidifies in time t second. What is the latent heat of fusion of the substance?

\$\begin{array}{l} Power=\dfrac { \theta }{ T } \\ \theta =mass\times latent\, \, heat \\ \theta =ml \\ P=\dfrac { { ML } }{ T } \Rightarrow l=\dfrac { { pt } }{ m } \end{array}\$

Q: How could latent heat be explained from the graph ? Explain in detail.

In order to initiate a phase change and complete it\$,\$ some energy in the form of heat is required\$.\$ This heat is called latent heat\$.\$ Thus all the energy supplied during this phase will be utilized only for phase change process and not for increasing the temperature\$.\$ Thus during the release of latent heat the temperature remains constant\$.\$