Calorimetry, Latent Heat & Mechanical Equivalent of Heat

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^{\circ}\text{C}$ to $120^{\circ}\text{C}$?

A lead bullet moving with velocity '$v$' strikes a wall and stops. $75\%$ of its energy is converted into heat. If the increase in the temperature is $\frac{v^2}{nJs}$, then the value of $n$ is

$\{s =$ specific heat of lead$, J =$ mechanical equivalent of heat$\}$

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ}\text{C}$ to $87^{\circ}\text{C}$. The rate of consumption of the gas is $\underline{\hspace{3em}}\text{ g/s}$.

(Take heat of combustion of gas $= 5.0 \times 10^{4}\text{ J/g}$, specific heat capacity of water $= 4200\text{ J/kg}\cdot{}^{\circ}\text{C}$)

$1$ g of water of volume $1$ cm$^{3}$ at $100^{\circ}$C is converted into steam of same temperature under normal atmospheric pressure ($10^{5}$ Pa). The volume of steam formed equals $1671$ cm$^{3}$. If the latent heat of vaporisation of water is $2256$ J/g, the change in internal energy is

The heat extracted out of $x$ gram of water initially at $50^{\circ}\text{C}$ to cool it down to $0^{\circ}\text{C}$ is sufficient to evaporate $(1000 - x)$ gram of water also initially at $50^{\circ}\text{C}$. The value of $x$ (closest integer) is ______. (Take latent heat of water $2256\text{ kJ/kg}$, specific heat capacity of water $4200\text{ J/kg.K}$)

$540$ gram of ice at $0^{\circ}$ C is mixed with $540$ gram of water at $90^{\circ}$ C. The final temperature of the mixture will be [Latent heat of fusion of water = 80 cal/g]

A piece of metal of 850 K is dropped into 1 kg of water at 300 K. If equilibrium temperature of water is 350 K then the heat capacity of the metal expressed in $\frac{J}{K}$ is $\Bigg($Sp. heat of water $= 1\ \frac{\text{cal}}{\text{g}\,{}^{\circ}\text{C}}\Bigg)$

$15$ g of ice at $0^{\circ}$C is added to a vessel containing water at $40^{\circ}$C. The mass of water and water equivalent of the vessel is $60$ g. Assuming that negligible heat is taken from the surroundings, the final temperature of the mixture will be

[ $L$ice $= 80$ cal/g, $S$water $= 1$ cal/g ]

10 kg of ice at $-10^{\circ}\text{C}$ is added to 100 kg of water to lower its temperature from 25 $^{\circ}\text{C}$. Consider no heat exchange to surroundings. The decrement to the temperature of water is $\underline{\hspace{3em}}\ {}^{\circ}\text{C}$. (specific heat of ice $= 2100\text{ J/kg.}{}^{\circ}\text{C}$, specific heat of water $= 4200\text{ J/kg.}{}^{\circ}\text{C}$, latent heat of fusion of ice $= 3.36 \times 10^{5}\text{ J/kg}$)

Density of water at $4^{\circ}\text{C}$ and $20^{\circ}\text{C}$ are $1000\text{ kg/m}^{3}$ and $998\text{ kg/m}^{3}$ respectively. The increase in internal energy of 4 kg of water when it is heated from $4^{\circ}\text{C}$ to $20^{\circ}\text{C}$ is ______ J.

(specific heat capacity of water $= 4.2\text{ kJ/kg K}$ and 1 atmospheric pressure $= 10^{5}\text{ Pa}$)

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool.

(Take g = 10 m/s2, specific heat of water = 4200 J/(kg K))

Match List - I with List - II.

List - I $\text{List - II}$

(A) Heat capacity of body (I) $\text{J kg}^{-1}$

(B) Specific heat capacity of body (II) $\text{J K}^{-1}$

(C) Latent heat (III) $\text{J kg}^{-1}\text{ K}^{-1}$

(D) Thermal conductivity (IV) $\text{J m}^{-1}\text{ K}^{-1}\text{ s}^{-1}$

Choose the correct answer from the options given below:

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is _______ grams. (Latent heat of fusion of lead $= 2.5 \times 10^{4}\text{ J kg}^{-1}$ and specific heat capacity of lead $= 125\text{ J kg}^{-1}\text{ K}^{-1}\Big)$

An amount of ice of mass $10^{-3}\text{ kg}$ and temperature $-10^{\circ}\text{C}$ is transformed to vapour of temperature $110^{\circ}\text{C}$ by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice $= 2100\text{ J kg}^{-1}\text{ K}^{-1}$, specific heat of water $= 4180\text{ J kg}^{-1}\text{ K}^{-1}$, specific heat of steam $= 1920\text{ J kg}^{-1}\text{ K}^{-1}$, Latent heat of ice $= 3.35 \times 10^{5}\text{ J kg}^{-1}$ and Latent heat of steam $= 2.25 \times 10^{6}\text{ J kg}^{-1}$)

A stationary object at $4^{\circ}\text{C}$ and weighing 3.5 kg falls from a height of 2000 m on snow mountain at $0^{\circ}\text{C}$. If the temperature of the object just before hitting the snow is $0^{\circ}\text{C}$ and the object comes to rest immediately then the quantity of ice that melts is (Acceleration due to gravity $= 10\text{ m/s}^{2}$, Latent heat of ice $= 3.5 \times 10^{5}\text{ J/kg}$)

A block of ice at $-10^{\circ}\text{C}$ is slowly heated and converted to steam at $100^{\circ}\text{C}$. Which of the following curves represent the phenomenon qualitatively:

A lead bullet moving with velocity ' $v$ ' strikes a wall and stops. If $50\%$ of its energy is converted into heat, then the increase in temperature is ( $s =$ specific heat of lead)

A water heater of power $2000\text{ W}$ is used to heat water. The specific heat capacity of water is $4200\text{ J kg}^{-1}\text{ K}^{-1}$. The efficiency of heater is $70\%$. Time required to heat $2\text{ kg}$ of water from $10^{\circ}\text{C}$ to $60^{\circ}\text{C}$ is _________ s.

(Assume that the specific heat capacity of water remains constant over the temperature range of the water).

Heat energy of 184 kJ is given to ice of mass 600 g at $-12^{\circ}\text{C}$. Specific heat of ice is $2222.3\text{ J kg}^{-1}\,{}^{\circ}\text{C}^{-1}$ and latent heat of ice is 336 $\text{kJ kg}^{-1}$

A. Final temperature of system will be 0$^{\circ}$ C.

B. Final temperature of the system will be greater than 0$^{\circ}$C.

C. The final system will have a mixture of ice and water in the ratio of 5: 1.

D. The final system will have a mixture of ice and water in the ratio of 1: 5.

E. The final system will have water only.

Choose the correct answer from the options given below:

A piece of metal at $850\text{ K}$ is dropped into $1\text{ kg}$ water at $300\text{ K}$. If the equilibrium temperature of water is $350\text{ K}$ then the heat capacity of the metal, expressed in $\text{J K}^{-1}$ is $(1\text{ cal} = 4.2\text{ J})$

Heat given to a body, which raises its temperature by 1ºC is known as

A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms$^{-}$1. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail? [Specific heat capacity of iron = 0.42 Jg$^{-}$1 $^{\circ}\text{C}^{-}$1]

A geyser heats water flowing at a rate of 2.0 kg per minute from 30$^{\circ}$C to 70$^{\circ}$ C. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min$^{-}$1.

[Heat of combustion = 8 $\times$ 103 Jg$^{-}$1, Specific heat of water = 4.2 Jg$^{-}$1 $^{\circ}\text{C}^{-}$1]

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is:

(Given: initial temperature of the bullet = 127$^{\circ}$C, Melting point of the bullet = 327$^{\circ}$C, Latent heat of fusion of lead = 2.5 $\times$ 104 J kg$^{-}$1, Specific heat capacity of lead = 125 J/kg K)

A copper block of mass 5.0 kg is heated to a temperature of 500$^{\circ}$C and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper: 0.39 J g$^{-}$1 $^{\circ}\text{C}^{-}$1 and latent heat of fusion of water: 335 J g$^{-}$1]

A block of ice of mass 120 g at temperature 0$^{\circ}$C is put in 300 g of water at 25$^{\circ}$ C. The x g of ice melts as the temperature of the water reaches 0$^{\circ}$ C. The value of x is _____________. [Use specific heat capacity of water = 4200 Jkg$^{-1}\text{K}^{-}$1, Latent heat of ice = 3.5 $\times$ 105 Jkg$^{-}$1]

The height of Victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall?

[Given 1 cal = 4.2 J and specific heat of water = 1 cal g$^{-}$1 $^{\circ}\text{C}^{-}$1]

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is:

The temperature of equal masses of three different liquids x, y and z are 10$^{\circ}$C, 20$^{\circ}$C and 30$^{\circ}$C respectively. The temperature of mixture when x is mixed with y is 16$^{\circ}$C and that when y is mixed with z is 26$^{\circ}$ C. The temperature of mixture when x and z are mixed will be:

The quantities of heat required to raise the temperature of two solid copper spheres of radii r1 and r2 (r1 = 1.5r2) through 1 K are in the ratio:

A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030 cal/(g –oC) (1 cal = 4.2 × 107 ergs) close to:

The specific heat of water

= 4200 J kg-1K-1 and the latent heat of

ice = 3.4 $\times$ 105 J kg–1. 100 grams of ice at

0oC is placed in 200 g of water at 25oC. The

amount of ice that will melt as the temperature

of water reaches 0oC is close to (in grams):

A calorimeter of water equivalent 20 g contains 180 g of water at 25oC. ‘m’ grams of steam at 100oC is mixed in it till the temperature of the mixure is 31oC. The value of ‘m’ is close to: (Latent heat of water = 540 cal g–1, specific heat of water = 1 cal g–1oC–1)

Three containers C1, C2 and C3 have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process)

The value of $\theta$ (in °C to the nearest integer) is ..........

M grams of steam at 100oC is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produced liquid water at 40oC [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g] the value of M is ____

One kg of water, at 20oC, heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 $\Omega$. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to: [Specific heat of water = 4200 J/(kgoC), Latent heat of water = 2260 kJ/kg]

A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)

When M1 gram of ice at –10oC (specific heat = 0.5 cal g–1oC–1) is added to M2 gram of water at 50°C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g–1 is:

When 100 g of a liquid A at 100oC is added to 50 g of a liquid B at temperature 75oC, the temperature of the mixture becomes 90oC. The temperature of the mixture, if 100 g of liquid A at 100oC is added to 50 g of liquid B at 50oC, will be:

A metal ball of mass 0.1 kg is heated upto 500oC and dropped into a vessel of heat capacity 800 JK–1 and containing 0.5 kg water. The initial temperature of water and vessel is 30oC. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg–1 K–1 and 400 Jkg–1 K–1]

Ice at –20oC is added to 50 g of water at 40oC. When the temperature of the mixture reaches 0oC, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2J/g/oC Specific heat of Ice = 2.1J/g/oC Heat of fusion of water at 0oC= 334J/g)

An unknown metal of mass 192 g heated to a temperature of 100oC was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4oC. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5oC. (Specific heat of brass is 394 J kg–1 K–1)

A thermally insulated vessel contains 150g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water = 2.10 × 106 J kg–1 and Latent heat of Fusion of water = 3.36 × 105 J kg–1)

In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150oC. Immediately, it is put into water of volume 150 cc at 27oC kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40oC. The specific heat of aluminium is: (take 4.2 Joule = 1 calorie)

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75oC. T is given by: (Given: room temperature = 30oC, specific heat of copper = 0.1 cal/gmoC)

200 g water is heated from 40oC to 60oC. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K):

An experiment takes 10 minutes to raise the temperature of water in a container from 0oC to 100oC and another 55 minutes to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of water to be 1 cal/goC, the heat of vapourization according to this experiment will come out to be:

Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160J/s. In how much time will the temperature of water rise from 27oC to 77oC? (Specific heat of water is 4.2 kJ/kg K and that of the container is negligible).

Given that 1 g of water in liquid phase has volume 1 cm$^{3}$ and in vapour phase 1671 cm$^{3}$ at atmospheric pressure and the latent heat of vaporization of water is 2256 J/g; the change in the internal energy in joules for 1 g of water at 373 K when it changes from liquid phase to vapour phase at the same temperature is:

500 g of water and 100 g of ice at 0°C are in a calorimeter whose water equivalent is 40 g. 10 g of steam at 100°C is added to it. Then water in the calorimeter is: (Latent heat of ice = 80 cal/g, Latent heat of steam = 540 cal/g)

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

Time taken by a $836\text{ W}$ heater to heat one litre of water from $10^{\circ}\text{C}$ to $40^{\circ}\text{C}$ is

Heat given to a body which raises its temperature by $1^{\circ}\text{C}$ is

If $1\text{ g}$ of steam is mixed with $1\text{ g}$ of ice, then the resultant temperature of the mixture is

Thermal capacity of 40 g of aluminium ($s = 0.2\text{ cal/g K}$) is

10 gm of ice cubes at $0^{\circ}\text{C}$ are released in a tumbler (water equivalent 55 g) at $40^{\circ}\text{C}$. Assuming that negligible heat is taken from the surroundings, the temperature of water in the tumbler becomes nearly ($L = 80\text{ cal/g}$)