eSaral - JEE | NEET | Class 8-10 Exam Prep App

A 100kg block is started with a speed of 2.0m/s on a long,

Question: A $100 \mathrm{~kg}$ block is started with a speed of $2.0 \mathrm{~m} / \mathrm{s}$ on a long, rough belt kept fixed in a horizontal position. The coefficient of kinetic friction between the block and the belt is $0.20$. (a) Calculate the change in the internal energy of the block-belt system as the block comes to a stop on the belt. (b) Consider the situation from a frame of reference moving at $2.0 \mathrm{~m} / \mathrm{s}$ along the initial velocity of the block. As seen from its f...

Figure (26.E1) shows a paddle wheel coupled to a mass of

Question: Figure (26.E1) shows a paddle wheel coupled to a mass of $12 \mathrm{~kg}$ through fixed frictionless pulleys. The paddle is immersed in a liquid of heat capacity $4200 \mathrm{~J} / \mathrm{K}$ kept in an adiabatic container. Consider a time interval in which the $12 \mathrm{~kg}$ block falls slowly through $70 \mathrm{~cm}$. (a) How much heat is given to the liquid? (b) How much work is done on the liquid? (c) Calculate the rise in the temperature of the liquid neglecting the heat ca...

A thermally insulated, closed copper vessel contains water at 15°C.

Question: A thermally insulated, closed copper vessel contains water at 15C. When the vessel is shaken vigorously for 15 minutes, the temperature rises to 17C. The mass of the vessel is 100g and that of the water is 200g. The specific heat capacities of copper and water are 420J/kg-K and 4200J/kg-K respectively. Neglect any thermal expansion. (a) How much heat is transferred to the liquid-vessel system? (b) How much work has been done on this system? (C) How much is the increase in internal ener...

A metal block of density 6000 kg/m2 and mass 1.2 kg

Question: A metal block of density $6000 \mathrm{~kg} / \mathrm{m}^{3}$ and mass $1.2 \mathrm{~kg}$ is suspended through a spring of spring constant $200 \mathrm{~N} / \mathrm{m}$. The spring-block system is dipped in water kept in a vessel. The water has a mass of $260 \mathrm{~g}$ and the block is at a height $40 \mathrm{~cm}$ above the bottom of the vessel. If the support to the spring is broken, what will be the rise in the temperature of the water. Specific heat capacity of the block is $25...

A copper cube of mas 200 g slides down on a rough inclined

Question: A copper cube of mas $200 \mathrm{~g}$ slides down on a rough inclined plane of inclination $37^{\circ}$ at a constant speed. Assume that any loss in mechanical energy goes into the copper block as thermal energy. Find the increase in the temperature of the block as it slides down through $60 \mathrm{~cm}$. Specific heat capacity of copper $=420 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$. Solution:...

A ball is droppedon a floor from a height of 2.0 m.

Question: A ball is droppedon a floor from a height of $2.0 \mathrm{~m}$. After the collision it rises up to a height of $1.5 \mathrm{~m}$. Assume that $40 \%$ of the mechanical energy lost goes as thermal energy into the ball. Calculate the rise in the temperature of the ball in the collision. Heat capacity of the ball is $800 \mathrm{~J} / \mathrm{K}$. Solution:...

Two blocks of masses 10 kg and 20 kg moving

Question: Two blocks of masses $10 \mathrm{~kg}$ and $20 \mathrm{~kg}$ moving at speeds of $10 \mathrm{~m} / \mathrm{s}$ and $20 \mathrm{~m} / \mathrm{s}$ respectively in opposite directions, approach each other and collide. If the collision is completely inelastic, find the thermal energy developed in the process. Solution:...

A block of mass 100 g slides on a rough horizontal surface.

Question: A block of mass $100 \mathrm{~g}$ slides on a rough horizontal surface. If the speed of the block decreases from 10 $\mathrm{m} / \mathrm{s}$ to $5 \mathrm{~m} / \mathrm{s}$, find the thermal energy developed in the process. Solution:...

A van of mass 1500 kg travelling at a speed of

Question: A van of mass $1500 \mathrm{~kg}$ travelling at a speed of $54 \mathrm{~km} / \mathrm{h}$ is stopped in $10 \mathrm{~s}$. Assuming that all the mechanical energy lost appears as thermal energy in the brake mechanism, find the average rate of production of thermal energy in cal/s. Solution:...

A brick weighing 4.0 kg is dropped into a 1.0 m

Question: A brick weighing $4.0 \mathrm{~kg}$ is dropped into a $1.0 \mathrm{~m}$ deep river from a height of $2.0 \mathrm{~m}$. Assuming that $80 \%$ of the gravitational potential energy is finally converted into thermal energy, find this thermal energy in calorie. Solution:...

A 50 kg man is running at a speed of 18 km/h.

Question: A $50 \mathrm{~kg}$ man is running at a speed of $18 \mathrm{~km} / \mathrm{h}$. If all the kinetic energy of the man can be used to increase the temperature of water from $20^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$, how much water can be heated with this energy? Solution:...

A bullet of mass 20 g enters into a fixed wooden block

Question: A bullet of mass $20 \mathrm{~g}$ enters into a fixed wooden block with a speed of $40 \mathrm{~m} / \mathrm{s}$ and stops in it. Find the change in internal energy during the process. Solution:...

On a winter day the temperature of the tap water is

Question: On a winter day the temperature of the tap water is $20^{\circ} \mathrm{C}$ whereas the room temperature is $5^{\circ} \mathrm{C}$. Water is stored in a tank of capacity $0.5 \mathrm{~m}^{3}$ for household use. If it were possible to use the heat liberated by the water to lift a $10 \mathrm{~kg}$ of mass vertically, how high can it be lifted as the water comes to the room temperature? Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$. Solution:...

Calculate the time required to heat 20kg

Question: Calculate the time required to heat $20 \mathrm{~kg}$ of water from $10^{\circ} \mathrm{C}$ to $35^{\circ} \mathrm{C}$ using an immersion heater rated $1000 \mathrm{~W}$. Assume that $80 \%$ of the power input is used to heat the water. Specific heat capacity of water= $4200 \mathrm{~J} / \mathrm{kg}^{-\mathrm{K}}$ Solution:...

1 kg of ice at 0°C is mixed with 1 kg of steam at 100°C.

Question: $1 \mathrm{~kg}$ of ice at $0^{\circ} \mathrm{C}$ is mixed with $1 \mathrm{~kg}$ of steam at $100^{\circ} \mathrm{C}$. What will be the composition of the systemwhen thermal equilibrium is reached? Latent heat of fusion of ice=3.36 $\times 10^{5} \mathrm{~J} / \mathrm{kg}$ and latent heat of vaporization of water $=2.26 \times 10^{6} \mathrm{~J} / \mathrm{kg}$. Solution:...

A cube of iron (density=8000 kg/m2 , specific heat capacity = 470 J/kg-K)

Question: A cube of iron (density $=8000 \mathrm{~kg} / \mathrm{m}^{3}$, specific heat capacity $=470 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$ ) is heated to a high temperature and is placed on a large block of ice at $0^{\circ} \mathrm{C}$. The cube melts the ice below it, displaces the water and sinks. In the final equilibrium position, its upper surface just goes inside the ice. Calculate the initial temperature of the cube. Neglect any loss of heat outside the ice and the cube. The density of i...

Indian style of cooling drinking water is to keep it in a pitcher having porous walls.

Question: 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 is contains $10 \mathrm{~kg}$ of water and $0.2 \mathrm{~g}$ 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...

Four 2cm × 2cm × 2cm cubes are taken out from a refrigerator are

Question: Four $2 \mathrm{~cm} \times 2 \mathrm{~cm} \times 2 \mathrm{~cm}$ cubes are taken out from a refrigerator are put in $200 \mathrm{ml}$ of a drink at $10^{\circ} \mathrm{C}$. (a) Find the temperature of the drink when the thermal equilibrium is attained in it. (b) If the ice cubes do not melt completely, find the amount melted. Assume that no heat is lost to the outside of the drink and that the container has negligible heat capacity. Density of ice $=900 \mathrm{~kg} / \mathrm{m}^{3}$,...

The temperatures of equal masses of three different liquids

Question: The temperatures of equal masses of three different liquids are $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are $12^{\circ} \mathrm{C}, 19^{\circ} \mathrm{C}$ and $28^{\circ} \mathrm{C}$ respectively. The temperature when $\mathrm{A}$ and $\mathrm{B}$ are mixed is $16^{\circ} \mathrm{C}$, and when $\mathrm{B}$ and $\mathrm{C}$ are mixed, it is $23^{\circ} \mathrm{C}$. What will be the temperature when $A$ and $C$ are mixed? Solution:...

A piece of iron of mass 100 g is kept inside

Question: A piece of iron of mass $100 \mathrm{~g}$ is kept inside a furnace for a long time and then put in a calorimeter of water equivalent $10 \mathrm{~g}$ containing $240 \mathrm{~g}$ of water at $20^{\circ} \mathrm{C}$. The mixture attains an equilibrium temperature of $60^{\circ} \mathrm{C}$. Find the temperature of the furnace. Specific heat capacity of iron $=470 \mathrm{~J} / \mathrm{kg}-{ }^{\circ} \mathrm{C}$. Solution:...

An aluminium vessel of mass 0.5 kg

Question: An aluminium vessel of mass $0.5 \mathrm{~kg}$ contains $0.2 \mathrm{~kg}$ of water at $20^{\circ} \mathrm{C}$. A block of iron of mass $0.2 \mathrm{~kg}$ at $100^{\circ} \mathrm{C}$ is gently put into the water. Find the equilibrium temperature of the mixture. Specific heat capacities of aluminium, iron and water are $910 \mathrm{~J} / \mathrm{kg}-\mathrm{K}, 470 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$ and $4200 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$ respectively. Solution:...

Use R=8.3 J/mol-K wherever required. A bucket full of water is placed in a room

Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A bucket full of water is placed in a room at $15^{\circ} \mathrm{C}$ with initial relative humidity $40 \%$. The volume of the room is $50 \mathrm{~m}^{3}$. (a) How much water will evaporate? (b) If the room temperature is increased by $5^{\circ} \mathrm{C}$ how much more water will evaporate? The saturation vapour pressure of water at $15^{\circ} \mathrm{C}$ and $20^{\circ} \mathrm{C}$ are $1.6 \mathrm{kPa}...

Use R=8.3 J/mol-K wherever required. The temperature and relative humidity are 300 K

Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The temperature and relative humidity are $300 \mathrm{~K}$ and $20 \%$ in a room of volume $50 \mathrm{~m}^{3}$. The floor is washed with water, $500 \mathrm{~g}$ of water sticking on the floor. Assuming no communication with the surrounding, find the relative humidity when the floor dries. The changes in temperature and pressure may be neglected. Saturation vapour pressure at $300 \mathrm{~K}=3.3 \mathrm{kP...

Use R=8.3 J/mol-K wherever required. The temperature and relative humidity in

Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The temperature and relative humidity in a room are $300 \mathrm{~K}$ and $20 \%$ respectively. The volume of the room is $50 \mathrm{~m}^{3}$. The saturation vapour pressure at $300 \mathrm{~K}$ is $3.3 \mathrm{kPa}$. Calculate the mass of the water vapour present in the room. Solution:...

Use R=8.3 J/mol-K wherever required. The temperature and humidity of

Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The temperature and humidity of air are $27^{\circ} \mathrm{C}$ and $50 \%$ on a particular day. Calculate the amount of vapour that should be added to 1 cubic meter of air to saturate it. The saturation vapour pressure at $27^{\circ} \mathrm{C}=3600$ $\mathrm{Pa}$. Solution:...

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