Latent Heat

Q. Steam at $100°\text{C}$ is passed into $20\text{g}$ of water at $10°\text{C}$. When water acquires a temperature of $80°\text{C}$, the mass of water present will be: [Take specific heat of water $=1{\text{cal g}}^{-1}{\text{C}}^{-1}$ and latent heat of steam $=540{\text{cal g}}^{-1}$]

1. $24\text{g}$
2. $31.5\text{g}$
3. $42.5\text{g}$
4. $22.5\text{g}$

Q. Ice starts forming in lake with water at $0^{\circ }$. When the atmospheric temperature is $-{10}^{\circ }C,$ if the time taken to form $1\text{cm}$ of ice be $7$ hours, then the time taken for the thickness of ice to change from $1\text{cm}$ to $2\text{cm}$ is

1. $14$ hours
2. $3.5$ hours
3. $7$ hours
4. $21$ hours

Q.

Why does ice at $0°\mathrm{C}$ appear colder than water at the same temperature?

Q.

540 g of ice at $0^{o}C$ is mixed with 540 g of water at ${80}^{o}C$. The final temperature of the mixture is

1. 0°C

2. 40°C

3. Less than 0°C

4. 80°C

Q. When $0.15\text{kg}$ of ice at $0^{\circ }\text{C}$ is mixed with $0.30\text{kg}$ of water at ${50}^{\circ }\text{C}$ in a container, the resulting temperature of the mixture is ${6.7}^{\circ }\text{C}$. Calculate the latent heat of fusion of ice. $(S_{water}=4186\text{J}{\text{kg}}^{–1}{\text{K}}^{-1})$

1. $3.34\times {10}^5\text{J}{\text{kg}}^{–1}$
2. $1.5\times {10}^5\text{J}{\text{kg}}^{–1}$
3. $2\times {10}^5\text{J}{\text{kg}}^{–1}$
4. $5.4\times {10}^5\text{J}{\text{kg}}^{–1}$

Q. A copper rod initially at room temperature ${20}^{\circ }\text{C})$ of non-uniform cross-section is placed between a steam chamber at ${100}^{\circ }\text{C}$ and ice-water chamber at $0^{\circ }\text{C}$

Identiity the correct statement (s):

1. Initially the rate of heat flow $\left(\frac{dQ}{dt}\right)$ will be maximum at section $B$
2. Initially the rate of heat flow $\left(\frac{dQ}{dt}\right)$ will be minimum at section $C$
3. At steady state the temperature gradient $\left|\left(\frac{dT}{dx}\right)\right|$ will be maximum at the section $B$
4. At steady state the rate of change of temperature $\left(\frac{dT}{dt}\right)$ for all sections will be equal to zero.

Q. A $10\text{kg}$ iron bar (specific heat $0.11{\text{cal/g}}^{\circ }\text{C}$) at ${80}^{\circ }\text{C}$ is placed on the block of ice. How much ice melts?
(Take latent heat of fusion as $80\text{cal/g}$)

1. $1\text{kg}$
2. $1.1\text{kg}$
3. $2.2\text{kg}$
4. $2\text{kg}$

Q. A thermally insulated vessel contains some water at $0^{\circ }\text{C}$. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given that the latent heat of vaporization of water at $0^{\circ }\text{C}$ is $21\times {10}^5\text{J/kg}$ and latent heat of freezing of water at $0^{\circ }\text{C}$ is $3.36\times {10}^5\text{J/kg}$. The maximum percentage of water vapour that will be solidified in this manner will be -

1. $86.2\%$
2. $33.6\%$
3. $21\%$
4. $24.36\%$

Q. $100\text{g}$ of water is heated from ${30}^{\circ }C$ to ${50}^{\circ }C$. Ignoring the slight expansion of the water, the change in its internal energy is $\left(\text{in kJ}\right)$ (specific heat of water is $4184\text{J/kg/K})$

Q. A steam engine intakes $50g$ of steam at ${100}^{o}C$ per minute and cools it down to ${20}^{o}C$. If latent heat of vaporization of steam is $540cal{g}^{-1}$, then the heat rejected by the steam engine per minute is ${10}^{3}cal$.
(Given : specific heat capacity of water : $1cal/g{}^{o}C$)

Q.

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in 20 minutes and 30 minutes. The ratio of their thermal conductivities will be

1. 1

2. 1.5

3. 2/3

4. 4

Q.

How does the interconversion of three states of matter takes place in terms of force of attraction and kinetic energy of the molecules?

Q. One end of a copper rod of length 1 m and area of cross section ${10}^{-3}{m}^2$ is immersed in boiling water at ${100}^{\circ }$C and the other end is in ice at $0^{\circ }$C. If the coefficient of thermal conductivity of copper is $92Cal{m}^{-1}{s}^{-1}{{}^{\circ }C}^{-1}$ and the latent heat of ice is 80 Cal $g^{-1}$, then the amount of ice which will melt in one minute is

1. 9.2 g
2. 8 g
3. 6.9 g
4. 5.4 g

Q.

Indian style of cooling drinking water is to keep it in a pitcher having porous walls. Water comes to the outer surface very slowly and evaporates. Most of the energy needed for evaporation is taken from the water itself and the water is cooled down. Assume that a pitcher contains 10 kg of water and 0.2 g of water comes out per second. Assuming no backward heat transfer from the atmosphere to the water, calculate the time in which the temperature decreases by $5^{\circ }C$. Specific heat capacity of water $=4200Jk{g}^{-1}$ ${}^{\circ }{C}^{-1}$ and latent heat of vaporization of water $=2.27\times {10}^{6}Jk{g}^{-1}$

Q.

Two conducting rods A and B of same length and cross-sectional area are connected (i) In series (ii) In parallel as shown. In both combination a temperature difference of ${100}^{\circ }$ C​ is maintained. If thermal conductivity of A is 3K and that of B is K then the ratio of heat current flowing in parallel combination to that flowing in series combination is

1. $\frac{16}{3}$

2. $\frac{3}{16}$

3. $\frac{1}{1}$

4. $\frac{1}{3}$

Q.

Define the term specific latent heat of fusion of ice. State its Si unit.

Q.

A quantity of heat required to change the unit mass of a solid substance, from solid state to liquid state, while the temperature remains constant, is known as the _______.

1. Latent heat

2. Hoar frost

3. Sublimation

4. Latent heat of fusion

Q. One $\text{gram}$ of ice is mixed with one $\text{gram}$ of steam. After thermal equilibrium is reached, the temperature of the mixture is
(Latent heat of fusion of ice; $L_{ice}=80\text{cal/g}$, latent heat of condensation of vapour; $L_V=540\text{cal/g}$)

1. ${100}^{\circ }\text{C}$
2. ${50}^{\circ }\text{C}$
3. $0^{\circ }\text{C}$
4. ${55}^{\circ }\text{C}$

Q.

Calculate the mass of ice needed to cool 150g of water contained in a calorimeter of mass 50g at ${32}^{o}C$ such that the final temperature is $5^{o}C$.

(Take specific heat capacity of water $c_w=4.2J/g^{o}C$ and latent heat capacity of ice $L=330J/g$)

Q. When $100\text{gms}$ of a liquid $A$, at $100{}^{\circ }\text{C}$ is added to $50\text{gms}$ of a liquid $B$ at temperature $75{}^{\circ }\text{C}$, the temperature of the mixture becomes $90{}^{\circ }\text{C}$. The temperature of the mixture, if $100\text{gms}$ of liquid $A$ at $100{}^{\circ }\text{C}$ is added to $50\text{gms}$ of liquid $B$ at $50{}^{\circ }\text{C}$ will be,

1. $85{}^{\circ }\text{C}$
2. $80{}^{\circ }\text{C}$
3. $70{}^{\circ }\text{C}$
4. $60{}^{\circ }\text{C}$

Q. A copper block of mass $2\text{kg}$ is heated to a temperature of ${500}^{\circ }\text{C}$ and then placed in a large block of ice at $0^{\circ }\text{C}$. What is the maximum amount of ice that can melt? The specific heat of copper is $400{\text{J kg}}^{-1}$ ${}^{\circ }{\text{C}}^{-1}$and latent heat of fusion of water is $3.5\times {10}^5{\text{J kg}}^{-1}$.

1. $\frac{4}{3}\text{kg}$
2. $\frac{8}{7}\text{kg}$
3. $\frac{6}{5}\text{kg}$
4. $\frac{10}{9}\text{kg}$

Q. Steam is passed into $56\text{g}$ of water at ${30}^{\circ }\text{C}$ till the temperature of mixture becomes ${90}^{\circ }\text{C}$. If the latent heat of steam is $536\text{cal/g}$, the mass of the mixture will be:
(Specific heat capacity of water is $1{\text{cal/g}}^{\circ }\text{C}$)

1. $80\text{g}$
2. $62.1\text{g}$
3. $60\text{g}$
4. $54\text{g}$

Q. A fin has $5mm$ diameter and $100mm$ length. The thermal conductivity of fin material is $400W{m}^{-1}{K}^{-1}.$ One end of the fin is maintained at ${130}^{\circ }C$ and its remaining surface is exposed to ambient air at ${30}^{\circ }C$. If the convective heat transfer coefficient is $40W{m}^{-2}{K}^{-1},$ the heat loss (in W) from the fin is

1. 
   $0.08$
2. 
   $5.0$
3. 
   $7.0$
4. 
   $7.8$

Q. The latent heat of vaporization of a substance is always:

1. greater than its latent heat of fusion.
2. greater than its latent heat of sublimation.
3. equal to its latent heat of fusion.
4. less than its latent heat of fusion.

Q. An electric immersion heater of $1.08\text{kW}$ is immersed in water. After it has reached a temperature of ${100}^{\circ }C$ , how much time will be require to produce $100\text{g}$ of steam ?

1. $50\text{s}$
2. $420\text{s}$
3. $105\text{s}$
4. $210\text{s}$

Q. On a cold winter day, the atmospheric temperature is $-\theta$ (on Celsius scale) which is below $0^{\circ }\text{C}$. A cylindrical drum of height $h$ made of a bad conductor is completely filled with water at $0^{\circ }\text{C}$ and is kept outside without any lid. Calculate the time taken for the whole mass of water to freeze. Thermal conductivity of ice is $K$ and its latent heat of fusion is $L$. Neglect expansion of water on freezing.

1. $\frac{\rho L{h}^2}{2K\theta }$
2. $\frac{3\rho L{h}^2}{2K\theta }$
3. $\frac{\rho L{h}^2}{4K\theta }$
4. $\frac{5\rho L{h}^2}{2K\theta }$

Q. $1\text{kg}$ ice at $-{20}^{\circ }\text{C}$ is mixed with $1\text{kg}$ steam at ${200}^{\circ }\text{C}$. The equilibrium temperature and mixture content is

1. ${80}^{\circ }\text{C}$, and mixture content $2\text{kg}$
2. ${110}^{\circ }\text{C}$, and mixture content $2\text{kg}$ steam
3. ${100}^{\circ }\text{C}$, and mixture content $\frac{10}{17}\text{kg}$ steam and $\frac{24}{17}\text{kg}$ water
4. ${100}^{\circ }\text{C}$, and mixture content $\frac{20}{27}\text{kg}$ steam and $\frac{34}{27}\text{kg}$ water

Q. Consider the following heating curve for water and match column $1$ with column $2$.


$\begin{array}{cc}\text{Column 1}& \text{Column 2}\\ \text{(a) Melting}& \left(i\right)CD\\ \text{(b) Vaporization}& \left(ii\right)BC\\ \text{(c) Boiling}& \left(iii\right)DE\end{array}$

1. $\left(a\right)\to \left(i\right),b\to \left(ii\right),c\to \left(iii\right)$
2. $\left(a\right)\to \left(ii\right),b\to \left(i\right),c\to \left(iii\right)$
3. $\left(a\right)\to \left(ii\right),b\to \left(iii\right),c\to \left(i\right)$
4. $a)\to (iii),b\to (ii),c\to (i)$

Q. An experiment takes $10\text{min}$ for an electric kettle to heat a certain quantity of water from $0^{\circ }\text{C}$ to ${100}^{\circ }\text{C}$. If it takes $54\text{min}$ to convert this water at ${100}^{\circ }\text{C}$ into steam, then latent heat of steam is:

1. $80\text{cal/gm}$
2. $540\text{cal/kg}$
3. $540\text{cal/gm}$
4. $80\text{cal/kg}$

Q.

Calculate the heat of fusion of ice from the following data for ice at $0^{\circ }C$ added to water. Mass of calorimeter = 60gm, mass of calorimeter + water = 460 gm, mass of calorimeter + water + ice = 618 gm, initial temperature of water = ${38}^{\circ }C$, final temperature of the mixture = $5^{\circ }C$. The specific heat of calorimeter = $0.10cal/g{/}^{\circ }C$. Assume that the calorimeter was also at $0^{\circ }C$ initially.

1. 78 cal/gm

2. 78 cal/kg

3. 86 cal/kg

4. 86 cal/gm