Area and Volume Expansion

Q.

A glass flask of volume one litre at $0^{\circ }C$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to ${100}^{\circ }C$. How much mercury will spill out, if coefficient of volume expansion of mercury is 1.82×${10}^{-4}{/}^{\circ }C$ and linear expansion of glass is 0.1×${10}^{-4}{/}^{\circ }C$ respectively

1. 21.2 cc

2. 15.2 cc

3. 1.52 cc

4. 2.12 cc

Q.

Whenever a liquid is heated in a container, expansion in liquid as well as container takes place. If r is the volume expansion coefficient of liquid and is coefficient of liner expansion. Match the entries of Column I and Column II
$$\begin{array}{cc}ColumnI& ColumnII\\ \left(i\right)Liquidlevelriseswithrespecttocontainer& \left(A\right)g=2a\\ \left(ii\right)Liquidlevelremainssamewithrespecttocontainer& \left(B\right)2\alpha <\gamma <3\alpha \\ \left(iii\right)Liquidleveldropswithrespecttocontainer& \left(C\right)g=3a\\ \left(iv\right)Liquidlevelremainssamewithrespecttoground& \left(D\right)g>3a\end{array}$$

1. (i) - (D), (ii) – (C), (iii) – (B), (iv) – (A)

2. (i) - (A), (ii) – (C), (iii) – (D), (iv) – (B)

3. (i) - (A), (ii) – (C), (iii) – (B), (iv) – (D)

4. (i) - (D), (ii) – (A), (iii) – (B), (iv) – (C)

Q. A circular hole in an aluminium plate is 1 cm in diameter at $0^{\circ }$. What is the diameter when the temperature of the plate is raised to ${100}^{\circ }$. (coefficient of linear expansion of aluminium $\alpha =2.55\times {10}^{-5}{/}^{\circ }$)

1. $(1.1051{)}^{1/2}cm$
2. $(10.0051{)}^{1/2}cm$
3. $(1.51{)}^{1/2}cm$
4. $(1.0051{)}^{1/2}cm$

Q.

An aluminium sphere is dipped into water at ${15}^{\circ }C({\gamma }_{aluminium}$ = $69\times {10}^{-6}{/}^{\circ }C;{\gamma }_{water}=214\times {10}^{-6}{/}^{\circ }C)$. If the temperature is increased, the force of buoyancy:

1. will increase
2. will decrease
3. will stay the same
4. will increase or decrease depending on the radius of the sphere

Q.

I received my favourite cologne, bottled in a metallic flask with a spherical cavity, on my birthday in December. I used it modestly only on special occasions, and found that I have finally emptied the bottle in mid-April, when the temperature had risen by ${25}^{\circ }C$ from December. If the metal's coefficient of superficial (area) expansion is $46\times {10}^{-5}{/}^{\circ }C$, how much extra cologne can I refill my bottle with, compared to the initial volume (answer in mL)?

1. 5 mL

2. 2 mL

3. 10 mL

4. 3.5 mL

Q.

You have with you, a mug of 500 mL, and a spoon of length 12 cm, both made of pure aluminum. When the AC in the room brings down the room temperature from ${34}^{\circ }C$, to ${16}^{\circ }C$ you find upon precise measurement, that the spoon got shorter by 0.00499 cms. What will be the new volume of the mug?

1. 501.12 mL
2. 499.38 mL
3. 498.54 mL
4. 502.3 mL

Q. If $k_1=$ rate constant at temperature $T_1$ and $k_2=$ rate constant at temperature $T_2$ for a first-order reaction, then which of the following relations is correct?
[$E_a=$ activation Energy]

1. $\log \frac{k_1}{k_2}=\frac{{2.303E}_a}{R}\left(\frac{T_2-T_1}{T_1{T}_2}\right)$
2. $\log \frac{k_2}{k_1}=\frac{E_a}{2.303R}\left(\frac{T_2-T_1}{T_1{T}_2}\right)$
3. $\log \frac{k_2}{k_1}=\frac{E_a}{2.303R}\left(\frac{T_1{T}_2}{T_2-T_1}\right)$
4. $\log \frac{k_1}{k_2}=\frac{E_a}{2.303R}\left(\frac{T_1{T}_2}{T_2-T_1}\right)$

Q.

A tumbler, made purely of iron, can be filled with 500 ml ($\sim 500c{m}^3$) of water during a spring temperature of ${20}^{\circ }C$. How much water (in volume) can you store in the tumbler in autumn, if the temperature drops to $8^{\circ }C$? ($\gamma Fe$ = $33.3$${/}^{\circ }C$).

1. 499.8 mL

2. None of these

3. 501.2 mL

4. 498.9 mL

Q. During summer, electrical wires sag due to _______.

1. thermal expansion of liquids
2. anomalous expansion
3. thermal expansion of gases
4. thermal expansion of solids

Q. A vessel of volume $1litre$ is filled with a liquid whose coefficient of volume expansion is $20$ times that of the vessel. At all temperatures if volume of air above the liquid is constant the volume of that empty space is:

1. $950cc$
2. $50cc$
3. $1000cc$
4. $500cc$

Q.

For a liquid, when heated in a vessel it is found that ${\gamma }_a=\frac{6}{7}{\gamma }_r$. The co-efficient of linear expansion of the vessel is :

1. $\frac{{\gamma }_r}{11}$
2. $\frac{{\gamma }_r}{14}$
3. $\frac{{\gamma }_r}{12}$
4. $\frac{{\gamma }_r}{21}$

Q.

If the coefficient of real expansion, ${\gamma }_r$ is 1% more than coefficient of apparent expansion, linear expansion coefficient of the material is :

1. $\frac{{\gamma }_r}{303}$
2. $\frac{100{\gamma }_r}{101}$
3. $\frac{101{\gamma }_r}{300}$
4. $\frac{101{\gamma }_r}{100}$

Q.

The remaining volume of a glass vessel is constant at all temperatures if $\frac{1}{x}$ of its volume is filled with mercury. The coefficient of volume is filled with mercury. The coefficient of volume expansion of mercury is 7 times that of glass. The value of $x$ should be

1. 5

2. 7

3. 6

4. 8

Q.

The ratio between the radius of the base and the height of a cylinder is $2:3$. Find the total surface area of the cylinder, if its volume is $1617c{m}^3$ .

Q. State and explain two uses of thermal expansion? ( 4 marks)

Q.

The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are ${\gamma }_1$ and ${\gamma }_2$ respectively. If the coefficient of linear expansion of the vessel A is $\alpha$, the coefficient of linear expansion of the vessel B is

1. $\frac{\alpha {\gamma }_1{\gamma }_2}{{\gamma }_1+{\gamma }_2}$
2. $\frac{{\gamma }_1-{\gamma }_2}{2\alpha }$
3. $\frac{{\gamma }_1-{\gamma }_2+\alpha }{3}$
4. $\frac{{\gamma }_1-{\gamma }_2}{3}+\alpha$

Q.

The relation between the coefficient of real expansion (${\gamma }_r$) and coefficient of apparent expansion (${\gamma }_a$) of a liquid and the coefficient linear expansion (${\alpha }_g$) of the material of the container is :

1. ${\gamma }_r={\alpha }_g+{\gamma }_{\alpha }$
2. ${\gamma }_r={\alpha }_g+3{\gamma }_{\alpha }$
3. ${\gamma }_r=3{\alpha }_g+{\gamma }_{\alpha }$
4. ${\gamma }_r=3({\alpha }_g+{\gamma }_{\alpha })$

Q. Water flows out horizontally from a hole with a velocity of $20m{s}^{-1}$. The area of cross section of the hole is 2.5$\times {10}^{-3}{m}^2$. Density of water is $1000kg{m}^{-3}$. Power needed to generate kinetic energy from water is

1. $2.5kW$
2. $20kW$
3. $1kW$
4. $10kW$

Q.

The ratio of coefficient of apparent expansions of a liquid in the containers A and B is 1:2. If $18\times {10}^{-6/0}C$ and $12\times {10}^{-6/0}C$ are the co-efficients of linear expansions of the containers A and B respectively, then the coefficient of real expansion of the liquid is

1. $6\times {10}^{-6/0}C$
2. $72\times {10}^{-6/0}C$
3. $30\times {10}^{-6/0}C$
4. $24\times {10}^{-6/0}C$

Q. $200g$ mass of a certain metal at ${83}^{\circ }C$ is immersed in $300g$ of water of ${30}^{\circ }C$. Final temperature of combination is ${33}^{o}C$.Calculate the specific heat capacity of metal. Assume that the specific heat capacity of water is $4.2J{g}^{-1}{K}^{-1}$

1. $0.189J{g}^{-1}{K}^{-1}$
2. $0.378J{g}^{-1}{K}^{-1}$
3. $3.78J{g}^{-1}{K}^{-1}$
4. $0.756J{g}^{-1}{K}^{-1}$

Q.

LIST -I	LIST - II
a) Mass of liquid expelled on heating	e)$\frac{m_1}{1+\gamma \Delta t}$
b) Corrected Barometric height	f)$\frac{d_1-d_2}{d_2\Delta t}$
c) Coefficient of real expansion of liquid	g) $\frac{{\gamma }_a{m}_1\Delta t}{1+{\gamma }_a\Delta t}$
d) Mass of liquid remaining on heating	h)$h_0[1-({\gamma }_r-\alpha \left)\Delta t\right]$

1. a-g, b-h, c-f, d-e
2. a-e, b-f, c-g, d-h.
3. a-f, b-g, c-h, d-e
4. a-h, b-e, c-g, d-h

Q.

A one-litre flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in the flask? Given the coefficient of linear expansion of glass is $9\times {10}^{-6}{}^{\circ }{C}^{-1}$ and the coefficient of volume expansion of mercury is $1.8\times {10}^{-4}{}^{\circ }{C}^{-1}$

1. $50c{m}^3$

2. $100c{m}^3$

3. $150c{m}^3$

4. $200c{m}^3$