Calorimetry

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JEE Main 2019

A thermally insulated vessel contains $150 g$ of water at $0^{\circ} C$ . Then, the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at $0^{\circ} C$ itself. The mass of evaporated water will be closest to (Latent heat of vaporisation of water $= 2.10 \times 1 0^{6} J kg^{- 1}$ and latent heat of fusion of water $= 3.36 \times 1 0^{5} J kg^{- 1}$ )

150 g

(B)

20 g

(C)

130 g

(D)

35 g

JEE Main 2019

LEVELJEE Main

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

Ice at $- 2 0^{\circ} C$ is added to $50 g$ of water at $4 0^{\circ} C$ . When the temperature of the mixture reaches $0^{\circ} C$ , it is found that $20 g$ of ice is still unmelted. The amount of ice added to the water was close to (Take, specific heat of water $= 4.2 J/g/^{\circ} C$ , specific heat of ice $= 2.1 J/g/^{\circ} C$ and heat of fusion of water at $0^{\circ} C = 334 J/g$ )

(A)

40 g

(B)

50 g

(C)

60 g

(D)

100 g

JEE Main 2020

LEVELJEE Main

The specific heat of water = $4200 J kg^{- 1} K^{- 1}$ and the latent heat of ice = $3.4 \times 1 0^{5} J kg^{- 1}$ . $100 g$ of ice at $0^{\circ} C$ is placed in $200 g$ of water at $2 5^{\circ} C$ . The amount of ice that will melt as the temperature of water reaches $0^{\circ} C$ is close to (in grams)

$M$ grams of steam at $10 0^{\circ} C$ is mixed with $200 g$ of ice at its melting point in a thermally insulated container. If it produces liquid water at $4 0^{\circ} C$ [heat of vaporisation of water is $540 cal/g$ and heat of fusion of ice is $80 cal/g$ ], the value of $M$ is ... .

JEE Main 2017

LEVELJEE Main

A copper ball of mass $100 g$ is at a temperature $T$ . It is dropped in a copper calorimeter of mass $100 g$ , filled with $170 g$ of water at room temperature. Subsequently, the temperature of the system is found to be $7 5^{\circ} C$ . $T$ is (Given, room temperature $= 3 0^{\circ} C$ , specific heat of copper $= 0.1 cal/g^{\circ} C$ )

(A)

88 5^{\circ} C

(B)

125 0^{\circ} C

(C)

82 5^{\circ} C

(D)

80 0^{\circ} C

JEE Main 2020

LEVELJEE Main

A calorimeter of water equivalent $20 g$ contains $180 g$ of water at $2 5^{\circ} C$ . ' $m$ ' grams of steam at $10 0^{\circ} C$ is mixed in it till the temperature of the mixture is $3 1^{\circ} C$ . The value of $m$ is close to (Take, latent heat of water $= 540 cal g^{- 1}$ , specific heat of water $= 1 cal g^{- 1}^{\circ} C^{- 1}$ )

(A)

2 g

(B)

3.2 g

(C)

2.6 g

(D)

4 g

JEE Main 2019

LEVELJEE Main

When $M_{1}$ gram of ice at $- 1 0^{\circ} C$ (specific heat $= 0.5 \text{ cal g}^{-1} ^\circ\text{C}^{-1}$ ) is added to $M_{2}$ gram of water at $5 0^{\circ} C$ , finally no ice is left and the water is at $0^{\circ} C$ . The value of latent heat of ice, in $cal g^{- 1}$ is

(A)

\frac{50 M _{2}}{M _{1}} - 5

(B)

\frac{50 M _{1}}{M _{2}} - 50

(C)

\frac{50 M _{2}}{M _{1}}

(D)

\frac{5 M _{2}}{M _{1}} - 5

JEE Main 2021

LEVELJEE Advanced

The temperature of equal masses of three different liquids $x, y$ and $z$ are $1 0^{\circ} C, 2 0^{\circ} C$ and $3 0^{\circ} C$ , respectively. The temperature of mixture when $x$ is mixed with $y$ is $1 6^{\circ} C$ and that when $y$ is mixed with $z$ is $2 6^{\circ} C$ . The temperature of mixture when $x$ and $z$ are mixed will be

(A)

28.3 2^{\circ} C

(B)

25.6 2^{\circ} C

(C)

23.8 4^{\circ} C

(D)

20.2 8^{\circ} C

JEE Main 2021

LEVELJEE Main

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

(A)

\frac{8}{3}

(B)

\frac{3}{8}

(C)

\frac{3}{4}

(D)

\frac{4}{3}

JEE Main 2019

LEVELJEE Main

A metal ball of mass $0.1 kg$ is heated upto $50 0^{\circ} C$ 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 $3 0^{\circ} C$ . What is the approximate percentage increment in the temperature of the water? [Take, specific heat capacities of water and metal are respectively $4200 Jkg^{- 1} K^{- 1}$ and $400 Jkg^{- 1} K^{- 1}$ ]

(A)

25%

(B)

15%

(C)

30%

(D)

20%

JEE Main 2019

LEVELJEE Advanced

An unknown metal of mass $192 g$ heated to a temperature of $10 0^{\circ} C$ was immersed into a brass calorimeter of mass $128 g$ containing $240 g$ of water at a temperature of $8. 4^{\circ} C$ . Calculate the specific heat of the unknown metal, if water temperature stabilises at $21. 5^{\circ} C$ . (Take, specific heat of brass is $394 J kg^{- 1} K^{- 1}$ )

(A)

916 J kg^{- 1} K^{- 1}

(B)

654 J kg^{- 1} K^{- 1}

(C)

1232 J kg^{- 1} K^{- 1}

(D)

458 J kg^{- 1} K^{- 1}

JEE Main 2020

LEVELJEE Main

Three containers $C_{1}$ , $C_{2}$ and $C_{3}$ have water at different temperatures. The table below shows the final temperature $T$ when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process) \begin{array}{|c|c|c|c|} \hline C_1 & C_2 & C_3 & T \\ \hline 1l & 2l & - & 60^\circ\text{C} \\ - & 1l & 2l & 30^\circ\text{C} \\ 2l & - & 1l & 60^\circ\text{C} \\ 1l & 1l & 1l & \theta \\ \hline \end{array} The value of $θ$ (in $^{\circ} C$ to the nearest integer) is ......

JEE Main 2021

LEVELJEE Advanced

Due to cold weather a $1 m$ water pipe of cross-sectional area $1 cm^{2}$ is filled with ice at $- 1 0^{\circ} C$ . Resistive heating is used to melt the ice. Current of $0.5 A$ is passed through $4 k Ω$ resistance. Assuming that, all the heat produced is used for melting, what is the minimum time required? [Given, latent heat of fusion for water/ice $= 3.33 \times 1 0^{5} J kg^{- 1}$ , specific heat of ice $= 2 \times 1 0^{3} J kg^{- 1}$ and density of ice $= 1 0^{3} kg/m^{3}$ ]

(A)

0.353 s

(B)

35.3 s

(C)

3.53 s

(D)

70.6 s

JEE Main 2021

LEVELJEE Main

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 $= 1 cal g^{- 1}^{\circ} C^{- 1}$ ]

(A)

0.14 7^{\circ} C

(B)

14.7 6^{\circ} C

(C)

1.47 6^{\circ} C

(D)

0.01 4^{\circ} C

LEVELJEE Advanced

An ice cube of mass 0.1 kg at 0°C is placed in an isolated container which is at 227°C. The specific heat S of the container varies with temperature T according to the empirical relation $S = A + B T$ , where $A = 100 cal/kg-K$ and $B = 2 \times 1 0^{- 2} cal/kg-K^{2}$ . If the final temperature of the container is 27°C, determine the mass of the container. (Latent heat of fusion for water = $8 \times 1 0^{4} cal/kg$ , specific heat of water = $1 0^{3} cal/kg-K$ ).

LEVELJEE Main

Earth receives $1400 W/m^{2}$ of solar power. If all the solar energy falling on a lens of area $0.2 m^{2}$ is focussed onto a block of ice of mass $280 g$ , the time taken to melt the ice will be ...... minutes. (Latent heat of fusion of ice $= 3.3 \times 1 0^{5} J/kg$ )

JEE Main 2006

LEVELJEE Advanced

In an insulated vessel, $0.05 kg$ steam at $373 K$ and $0.45 kg$ of ice at $253 K$ are mixed. Find the final temperature of the mixture (in kelvin). Given, $L_{fusion} = 80 cal/g = 336 J/g$ , $L_{vaporisation} = 540 cal/g = 2268 J/g$ , $S_{ice} = 2100 J/kg K = 0.5 cal/g-K$ and $S_{water} = 4200 J/kg K = 1 cal/g-K$ .

JEE Advanced 2016

LEVELJEE Advanced

A water cooler of storage capacity 120 litres can cool water at a constant rate of $P$ watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30°C and the entire stored 120 litres of water is initially cooled to 10°C. The entire system is thermally insulated. The minimum value of $P$ (in watts) for which the device can be operated for 3 hours is (Specific heat of water is $4.2 kJ kg^{- 1} K^{- 1}$ and the density of water is $1000 kg m^{- 3}$ )

A piece of ice (heat capacity = $2100 Jkg^{- 1}^{\circ} C^{- 1}$ and latent heat = $3.36 \times 1 0^{5} J kg^{- 1}$ ) of mass $m$ gram is at $- 5^{\circ} C$ 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 g of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is

JEE Main 2005

LEVELBoard

Calorie is defined as the amount of heat required to raise temperature of 1 g of water by 1°C and it is defined under which of the following conditions ?

(A)

From 14.5°C to 15.5°C at 760 mm of Hg

(B)

From 98.5°C to 99.5°C at 760 mm of Hg

(C)

From 13.5°C to 14.5°C at 76 mm of Hg

(D)

From 3.5°C to 4.5°C at 76 mm of Hg

JEE Main 2005

LEVELJEE Main

Water of volume 2 L in a container is heated with a coil of 1 kW at 27°C. The lid of the container is open and energy dissipates at a rate of 160 J/s. In how much time temperature will rise from 27°C to 77°C? [Specific heat of water is 4.2 kJ/kg]

300 g of water at $2 5^{\circ} C$ is added to 100 g of ice at $0^{\circ} C$ . The final temperature of the mixture is ......... $^{\circ} C$ .

LEVELJEE Main

2 kg of ice at –20°C is mixed with 5 kg of water at 20°C in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are 1 kcal/kg /°C and 0.5 kcal/kg /°C while the latent heat of fusion of ice is 80 kcal/kg

Liquid oxygen at 50 K is heated to 300 K at constant pressure of 1 atm. The rate of heating is constant. Which of the following graphs represent the variation of temperature with time?

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

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

Calorie is defined as the amount of heat required to raise temperature of 1 g of water by 1°C and it is defined under which of the following conditions ?

Water of volume 2 L in a container is heated with a coil of 1 kW at 27°C. The lid of the container is open and energy dissipates at a rate of 160 J/s. In how much time temperature will rise from 27°C to 77°C? [Specific heat of water is 4.2 kJ/kg]

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 300 g of water at 25∘C is added to 100 g of ice at 0∘C. The final temperature of the mixture is .........∘C.

Liquid oxygen at 50 K is heated to 300 K at constant pressure of 1 atm. The rate of heating is constant. Which of the following graphs represent the variation of temperature with time?

300 g of water at $2 5^{\circ} C$ is added to 100 g of ice at $0^{\circ} C$ . The final temperature of the mixture is ......... $^{\circ} C$ .