Calorimetry

Q.

What is water equivalent?​

Q. $100\text{g}$ of ice (latent heat $80{\text{cal g}}^{-1}$), at $0^{\circ }\text{C}$ is mixed with $100\text{g}$ of water (specific heat $1{\text{cal g}}^{-1}{/}^{\circ }\text{C}$ ) at ${80}^{\circ }\text{C}$. The final temperature of the mixture will be

1. ${40}^{\circ }\text{C}$
2. $0^{\circ }\text{C}$
3. ${80}^{\circ }\text{C}$
4. $<0^{\circ }\text{C}$

Q. The temperatures of equal masses of three different liquids $A,B$ and $C$ are ${12}^{\circ }\text{C},{19}^{\circ }\text{C}$ and ${28}^{\circ }\text{C}$ respectively. The temperature when $A$ and $B$ are mixed is ${16}^{\circ }\text{C}$, when $B$ and $C$ are mixed is ${23}^{\circ }\text{C}$. What is the temperature when $A$ and $C$ are mixed?

1. ${31}^{\circ }\text{C}$
2. ${20.26}^{\circ }\text{C}$
3. ${19.5}^{\circ }\text{C}$
4. ${28}^{\circ }\text{C}$

Q.

Predict the nature of following changes whether exothermic or endothermic?

Dissolution of ammonium chloride in water.

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

1. ${31.54}^{\circ }C$
2. ${21.54}^{\circ }C$
3. ${19}^{\circ }C$
4. ${15.68}^{\circ }C$

Q. $2\text{kg}$ ice at $-{20}^{\circ }\text{C}$ is mixed with $5\text{kg}$ water at ${20}^{\circ }\text{C}$. Then final amount of water in the mixture would be
Given specific heat of ice $=0.5{\text{cal/g}}^{\circ }\text{C}$,
Specific heat of water $=1{\text{cal/g}}^{\circ }\text{C}$,
Latent heat of fusion for ice $=80\text{cal/g}$.

1. $6\text{kg}$
2. $5\text{kg}$
3. $4\text{kg}$
4. $2\text{kg}$

Q.

What Is Mayers Formula?

Q.

The internal energy change (in J) when $90g$ of water undergoes complete evaporation at $100ºC$ is

( Given :$∆H_{vap}$for water at$373k=41kJ/mol,R=8.314J{K}^{-1}mo{l}^{-1})$,

Q. Two litres of water at initial temperature of ${27}^{\circ }\text{C}$ is heated by a heater of power $1\text{kW}$ in a kettle. If the lid of the kettle is open, then heat energy is lost at a constant rate of $160\text{J/s}$. The time in which the temperature will rise from ${27}^{\circ }\text{C}$ to ${77}^{\circ }\text{C}$ is (specific heat of water $=4.2\text{kJ/kg}$).

1. $5\text{min}20\text{sec.}$
2. $8\text{min}20\text{sec.}$
3. $10\text{min}40\text{sec.}$
4. $8\text{min}50\text{sec.}$

Q. $1\text{kg}$ of ice at $-{10}^{\circ }\text{C}$ is mixed with $4.4\text{kg}$ of water at ${30}^{\circ }\text{C}$. The final temperature of mixture is

Given specific heat of ice $=0.5{\text{cal/g}}^{\circ }\text{C}$,
Specific heat of water $=1{\text{cal/g}}^{\circ }\text{C}$,
Latent heat of fusion for ice $=80\text{cal/g}$.

1. ${2.3}^{\circ }\text{C}$
2. ${4.4}^{\circ }\text{C}$
3. ${5.3}^{\circ }\text{C}$
4. ${8.7}^{\circ }\text{C}$

Q. A liquid at ${30}^o$C is poured very slowly into a Calorimeter that is at temperature of ${110}^o$C. The boiling temperature of the liquid is ${80}^o$C. It is found that the first $5$gm of the liquid completely evaporates. After pouring another $80$ gm of the liquid the equilibrium temperature is found to be ${50}^o$C. The ratio of the Latent heat of the liquid to its specific heat will be${}^{\circ }C$. (Neglect the heat exchange with surrounding)

Q. Figure shows the temperature variation when heat is added continuously to a specimen of ice $\left(10\text{g}\right)$ at $-{40}^{\circ }\text{C}$ at constant rate. (Specific heat of ice $=0.53{\text{cal/g}}^{\circ }\text{C}$ and $L_{\text{ice}}=80\text{cal/g},L_{\text{water}}=540\text{cal/g)}$

$\begin{array}{cc}\text{Column - I}& \text{Column - II}\\ \left(A\right)\text{Value of}{Q}_1\text{(in cal)}& \left(P\right)800\\ \left(B\right)\text{Value of}{Q}_2\text{(in cal)}& \left(Q\right)1000\\ \left(C\right)\text{Value of}{Q}_3\text{(in cal)}& \left(R\right)5400\\ \left(D\right)\text{Value of}{Q}_4\text{(in cal)}& \left(S\right)212\\ & \left(T\right)900\end{array}$

1. $A\to P;B\to S;C\to Q;D\to R$
2. $A\to S;B\to P;C\to Q;D\to R$
3. $A\to S;B\to P;C\to Q;D\to T$
4. $A\to P;B\to S;C\to R;D\to Q$

Q. A bullet of mass $10\text{g}$ moving with a speed of $20\text{m/s}$ hits an ice block of mass $990\text{g}$ kept on a floor and gets stuck in it. How much ice will melt if $50\%$ of the lost KE goes to ice? (initial temperature of the ice block and bullet = $0^{\circ }\text{C}$)

1. $0.001\text{g}$
2. $0.002\text{g}$
3. $0.003\text{g}$
4. $0.004\text{g}$

Q. $5\text{g}$ of steam at $100{}^{\circ }\text{C}$ is passed into $6\text{g}$ of ice at $0{}^{\circ }\text{C}$. If the latent heat of steam and ice are $540\text{cal/g}$ and $80\text{cal/g}$ respectively and specific heat capacity of water is $1\text{cal}/\text{g}{}^{\circ }\text{C}$, then the final temperature of the mixture is

1. $0{}^{\circ }\text{C}$
2. $100{}^{\circ }\text{C}$
3. $50{}^{\circ }\text{C}$
4. $30{}^{\circ }\text{C}$

Q. A beaker contains 200 gm of water. The heat capacity of the beaker is equal to that of 20 gm of water. The
initial temperature of water in the beaker is ${20}^{\circ }C.$ If 440 gm of hot water at ${92}^{\circ }C$ is poured in it, the final
temperature (neglecting radiation loss) will be nearest to

1. 
2. 
3. 
4. 

Q. The following figure represents the temperature versus time plot for a given amount of a substance when heat energy is supplied to it at a fixed rate and at a constant pressure. Which part of the plot represents phase change?

1. $a$ to $b$ and $e$ to $f$
2. $d$ to $e$ and $e$ to $f$
3. $b$ to $c$ and $c$ to $d$
4. $b$ to $c$ and $d$ to $e$

Q.

Calculate the time required to heat 20 kg of water from ${10}^{\circ }C$ to ${35}^{\circ }C$ using an immersion heater rated 1000 W. Assume that 80% of the power input is used to heat the water. Specific heat capacity of water $=4200Jk{g}^{-1}{K}^{-1}$.

Q.

A metal block of density 6000 kg $m^{-3}$ and mass 1.2 kg is suspended through a spring of spring constant 200 N $m^{-1}$. The spring-block system is dipped in water kept in a vessel. The water has a mass of 260 g and the block is at a height 40 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 250 J $k{g}^{-1}{K}^{-1}$ and that of water is 4200 J $k{g}^{-1}{K}^{-1}$. The heat capacities of the vessel and the spring are negligible.

Q. Three rods of identical cross - section and lengths are made of three different materials of thermal conductivity $K_1,K_2\text{and}{K}_3,$ respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at ${100}^{\circ }\text{C}$ and the other at $0^{\circ }\text{C}$ (see figure). If the joints of the rod are at ${70}^{\circ }\text{C}$ and ${20}^{\circ }\text{C}$ in steady state and there is no loss of energy from the surface of the rod, the correct relationship between $K_1,K_2\text{and}{K}_3$ is :

1. $K_1:K_3=2:3,K_2:K_3=2:5$
2. $K_1<K_2<K_3$
3. $K_1:K_2=5:2,K_1:K_3=3:5$
4. $K_1>K_2>K_3$

Q. $20\text{gm}$ ice at $-10{}^{\circ }\text{C}$ is mixed with $m\text{gm}$ steam at $100{}^{\circ }\text{C}$. The minimum value of $m$ so that finally all ice and steam converts into water is
$[$ Use, specific heat and latent heat as $C_{ice}=0.5\text{cal/gm}{}^{\circ }\text{C},C_{\text{water}}=1\text{cal/gm}{}^{\circ }\text{C},L_{melt}$ $=80\text{cal/gm}$ and $L_{vapor}$ $=540\text{cal/gm}$ $]$

1. $\frac{185}{27}\text{gm}$
2. $\frac{85}{32}\text{gm}$
3. $\frac{135}{17}\text{gm}$
4. $\frac{113}{17}\text{gm}$

Q. Work done in converting one gram of ice at $–{10}^{\circ }C$ into steam at ${100}^{\circ }C$ is

1. 6056 J
2. 721 J
3. 3045 J
4. 616 J

Q. A ball of thermal capacity $10\text{cal}{/}^{\circ }C$ is heated to the temperature of furnace. It is then transferred into a vessel containing water. The water equivalent of vessel and the contents is $200\text{gm}$. The temperature of the vessel and its contents rises from ${10}^{\circ }C$ to ${40}^{\circ }C$. What is the temperature of furnace?

1. ${640}^{\circ }C$
2. ${64}^{\circ }C$
3. ${600}^{\circ }C$
4. ${100}^{\circ }C$

Q.

An aluminium vessel of mass 0.5 kg contains 0.2 kg of water at ${20}^{\circ }C$. A block of iron of mass 0.2 kg at ${100}^{\circ }C$ is gently put into the water. Find the equilibrium temperature of the mixture. Specific heat capacities of aluminium, iron and water are $910K{g}^{-1}{K}^{-1}470Jk{g}^{-1}{K}^{-1}$ and $4200Jk{g}^{-1}{K}^{-1}$ respectively.

Q. A calorimeter contains $0.2\text{kg}$ of water at ${30}^{\circ }\text{C}$. If $0.1\text{kg}$ of water at ${60}^{\circ }\text{C}$ is added to it, the mixture is well stirred and the resulting temperature is found to be ${35}^{\circ }\text{C}$. The thermal capacity of the calorimeter is

1. $4200\text{J/K}$
2. None of these
3. $6300\text{J/K}$
4. $1260\text{J/K}$

Q.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Assertion A: When a rod lying freely is heated, no thermal stress is developed in it. Reason $R$: On heating, the length of the rod increases In the light of the above statements, choose the correct answer from the options given below:

1. A is true but R is false

2. Both A and R are true and R is the correct explanation of A

3. Both A and R are true but R is NOT the correct explanation of A

4. A is false but R is true

Q.

A piece of iron of mass 100 g is kept inside a furnace for a long time and then put in a calorimeter of water equivalent 10 g containing 240 g of water at ${20}^{\circ }C$. The mixture attains an equilibrium teperature of ${60}^{\circ }C.$ Find the temperature of the furnace. Specific heat capacity of iron $=470Hk{g}^{-1}{}^{\circ }{C}^{-1}.$

Q. The water equivalent of $20\text{g}$ of aluminium (specific heat $0.2{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$) , is

1. $40\text{g}$
2. $4\text{g}$
3. $8\text{g}$
4. $160\text{g}$

Q. Calculate the least amount of work that must be done to freeze 1g of water at 0°C by means of refrigerator. Temperature of surroundings is 27°C. How much heat is passed into the surroundings?

Q. An ice block at $0^{\circ }\text{C}$ and of mass $m$ is dropped from height ${}^{\prime }{h}^{\prime }$ such that the loss in gravitational potential energy of the block is exactly equal to the heat required to completely melt the ice. Taking latent heat of fusion of ice, $L=80\text{cal/gm}$, acceleration due to gravity $g=10{\text{m/s}}^2$ and mechanical equivalent of heat $J=4.2\text{J/cal}$. find the value of ${}^{\prime }{h}^{\prime }$.

1. $18.20\text{km}$
2. $9.10\text{km}$
3. $33.60\text{km}$
4. $45.50\text{km}$

Q.

80 gm of water at ${30}^{\circ }C$ are poured on a large block of ice at $0^{\circ }C$. The mass of ice that melts is

1. 30 gm

2. 80 gm

3. 1600 gm

4. 150 gm