Latent Heat

Q.

M grams of steam at 100⁰C is mixed with 200g of ice at its melting point in a thermally insulated container. If it produces liquid water at 40⁰ C[heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g ], the value of M is __.

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; $L_V=540\text{cal/g}$,
Specific heat capacity of water; $c=1{\text{cal/g}}^{\circ }\text{C}$)

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

Q.

The value of Latent heat of fusion of ice is ………………

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. A lead bullet strikes against a steel armor plate with the velocity of 300 meter/second. If the bullet, assuming that the impact is perfectly inelastic find the rise in temperature of the bullet. Assume that the heat produced is shared equally between the bullet and the target, specific heat of lead = $0.03cal/g{/}^{\circ }C$

1. ${178.6}^{\circ }C$
2. ${78.6}^{\circ }C$
3. ${2780.6}^{\circ }C$
4. ${100.6}^{\circ }C$

Q. $2\text{kg}$ of ice at $-{20}^{\circ }\text{C}$ is mixed with $5\text{kg}$ of water at ${20}^{\circ }\text{C}$ in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that specific heats of water and ice are $1\text{Kcal}{\text{kg}}^{-1}$ ${}^{\circ }{\text{C}}^{-1}$ and $0.5\text{Kcal}{\text{kg}}^{-1}$ ${}^{\circ }{\text{C}}^{-1}$ while the latent heat of fusion of ice is $80\text{kcal/kg}$

1. $7\text{kg}$
2. $6\text{kg}$
3. $4\text{kg}$
4. $2\text{kg}$

Q. In the figure shown, $AB$ is a rod of length $30\text{cm}$ and area of cross-section $1.0{\text{cm}}^2$ and thermal conductivity 336 S.I. units. The ends $A$ & $B$ are maintained at temperatures ${20}^{\circ }\text{C}$ and ${40}^{\circ }\text{C}$ respectively. A point $C$ of this rod is connected to a box $D$, containing ice at $0^{\circ }\text{C}$, through a highly conducting wire of negligible heat capacity. Find the initial rate (in $\text{mg/s}$) at which ice melts in the box. [Assume latent heat of fusion for ice $L_f=80\text{cal/gm}$]

Q. $1\text{kg}$ of ice at $0^{\circ }\text{C}$ is mixed with $1\text{kg}$ of steam at ${100}^{\circ }\text{C}$. Find the mass of steam when the mixture has reached thermal equilibrium.
$[L_{fusion,ice}=3.36\times {10}^5\text{J/kg},$$L_{vaporization,water}=2.26\times {10}^6\text{J/kg},$$C_{water}=4200\text{J/kg-K}]$

1. $800\text{g}$
2. $665\text{g}$
3. $500\text{g}$
4. $400\text{g}$

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. Compared to a burn due to water at ${100}^{\circ }C,$ a burn due to steam at ${100}^{\circ }C,$ is _______.

1. More dangerous
2. Less dangerous
3. Equally dangerous
4. not dangerous

Q. Steam at ${100}^{o}C$ is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at ${15}^{o}C$ till the temperature of the calorimeter and its contents rises to ${80}^{o}C.$ The mass of the steam condensed in kg is

(IIT JEE 1986)

1. 0.13
2. 0.065
3. 0.26
4. 0.135

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. 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 is taken from the water itself and the water is cooled down. If pitcher has $10\text{kg}$ of water, find the time in which the temperature of water falls by $5^{\circ }\text{C}$. The approximate rate of vaporisation is $5{\text{g min}}^{-1}$ $(C_w=1{\text{cal/g-}}^{\circ }\text{C},L_v=540\text{cal/g})$

1. $20\text{min}10\text{s}$
2. $18\text{min}20\text{s}$
3. $14\text{min}12\text{s}$
4. $\text{none of these}$

Q. A ball at ${40}^{\circ }C$ is dropped from a height of $5\text{km}$. The ball is heated due to air resistance and it completely melts just before reaching the ground. The specific heat capacity of the ball is $125{\text{J kg}}^{-1}{{}^{\circ }C}^{-1}$ and melting point is ${340}^{\circ }\text{C}$. Then, the latent heat of the fusion of the ball (in ${\text{kJ kg}}^{-1}$) is

[Take $g=10{\text{m/s}}^2$]

Q. In a heating experiment, it was noted that the temperature of liquid in a beaker rose at $4.0\text{K}$ per minute just before it began to boil, and $40$ minutes later, all the liquid had boiled away.
For this liquid, what is the value of ratio
$\frac{\text{specific heat capacity}}{\text{specific latent heat of vapourisation}}$ (in SI units)?

1. $\frac{1}{10}$
2. $\frac{1}{40}$
3. $\frac{1}{160}$
4. $\frac{1}{640}$

Q. Compared to a burn due to water at ${100}^{\circ }C,$ a burn due to steam at ${100}^{\circ }C,$ is _______.

1. More dangerous
2. Less dangerous
3. Equally dangerous
4. not dangerous