Area and Volume Expansion

Q.

A piece of metal floats in mercury. The coefficients of volume expansion of the metal and mercury are ${\gamma }_1$ and ${\gamma }_2$ respectively. If their temperature is increased by $\Delta T$, the fraction of the volume of metal submerged in mercury changes by a factor

1. $\left(\frac{1+{\gamma }_2\Delta T}{1+{\gamma }_1\Delta T}\right)$

2. $\left(\frac{1+{\gamma }_2\Delta T}{1-{\gamma }_1\Delta T}\right)$

3. $\left(\frac{1-{\gamma }_2\Delta T}{1+\gamma \Delta T}\right)$

4. $\frac{{\gamma }_2}{{\gamma }_1}$

Q.

The density of a liquid of coefficient of cubical expansion $\gamma$ is $\rho$ at $0^{\circ }C$. When the liquid is heated to a temperature T, the change in density will be

1. $-\frac{\rho (1+\gamma T)}{\gamma T}$

2. $\frac{-\rho \gamma T}{(1+\gamma T)}$

3. $\frac{\rho \gamma T}{(1+\gamma T)}$

4. $\frac{\rho (1+\gamma T)}{\gamma T}$

Q. A mercury-in-glass thermometer has a stem of internal diameter 0.06 cm and contains 43 g of mercury. The mercury thread expands by 10 cm when the temperature changes from $0^{\circ }C$ to ${50}^{\circ }C$. Find the coefficient of cubical expansion of mercury. Relative density of mercury = 13.6 and ${\alpha }_{glass}=9\times {10}^{-6}{K}^{-1}$

1. 
2. 
3. 
4. 

Q. A solid ball of metal has a spherical cavity inside it. The ball is heated. The volume of the cavity will

1. Increase
2. Decrease
3. Remain unchanged
4. Have its shape changed

Q. A metal plate is heated. State three factors on which the increase in its area will depend.

Q.

Calculate the increase in the volume of a liquid when heated to 40⁰C. Given that the original volume of liquid is 2 liters and its volume expansion coefficient is $12\times {10}^{-4}{/}^{0}C$.

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. $150c{m}^3$

3. $100c{m}^3$

4. $200c{m}^3$

Q. A piece of stone of mass $200\text{g}$ sinks to the bottom in water contained in a measuring cylinder and the water level in cylinder rises from $30\text{mL}$ to $60\text{mL}$. Calculate the RD of stone. ($g$ = $10{\text{m/s}}^2$, density of water = $1000{\text{kg/m}}^3$)

1. $6.66$
2. $6.86$
3. $6.33$
4. $4.66$

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. 2.12 cc

2. 21.2 cc

3. 15.2 cc

4. 1.52 cc

Q.

A sphere of diameter 7.0 cm and mass 266.5 g floats in a bath of a liquid. As the temperature is raised, the sphere begins to sink at a temperature of ${35}^{\circ }C$. If the density of the liquid is $1.527g/c{m}^3$ at $0^{\circ }C$, find the coefficient of cubical expansion of the liquid. Neglect the expansion of the sphere.

1. 2.32 × 10^-4/°C

2. 1.22 × 10^-4/°C

3. 8.28 × 10^-4/°C

4. 6.36 × 10^-4/°C

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.

A piece of metal floats in mercury. The coefficients of volume expansion of the metal and mercury are ${\gamma }_1$ and ${\gamma }_2$ respectively. If their temperature is increased by $\Delta T$, the fraction of the volume of metal submerged in mercury changes by a factor

1. $\left(\frac{1+{\gamma }_2\Delta T}{1+{\gamma }_1\Delta T}\right)$

2. $\frac{{\gamma }_2}{{\gamma }_1}$

3. $\left(\frac{1+{\gamma }_2\Delta T}{1-{\gamma }_1\Delta T}\right)$

4. $\left(\frac{1-{\gamma }_2\Delta T}{1+\gamma \Delta T}\right)$

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. 502.3 mL

3. 499.38 mL

4. 498.54 mL

Q.

On a hot day in Jaipur, an oil trucker loaded 40 kL (kilolitres) of diesel fuel. On his way to Shimla, he encounters a temperature drop of ${20}^{\circ }C$, where he stopped and delivered the entire load. How many litres did he deliver? The γ for diesel is $9.50\times {10}^{-4}{/}^{\circ }C$ and α for his steel truck is $11\times {10}^{-6}{/}^{\circ }C$. If you find that the volume has decreased, think about who is paying for the "missing” diesel.

1. 39, 240 L

2. 39, 810 L

3. 40, 000 L

4. 40, 126 L

Q.

The coefficient of expansion of a crystal in one direction (x-axis) is $2.0\times {10}^{-6}{K}^{-1}$ and that in the other two perpendicular directions (y and z-axes) is $1.6\times {10}^{-6}{K}^{-1},$What is the coefficient of cubical expansion of the crystal?

1. $2.0\times {10}^{-6}{K}^{-1}$

2. $5.2\times {10}^{-6}{K}^{-1}$

3. $1.8\times {10}^{-6}{K}^{-1}$

4. $1.6\times {10}^{-6}{K}^{-1}$

Q.

A gas in an airtight container is heated from ${25}^{\circ }C$ to ${90}^{\circ }C$. The density of the gas will:
( Consider there is a negligible expansion of container)

1. Increase considerably

2. Remain the same

3. Increase slightly

4. Decrease slightly

Q. A piece of metal weighs 46 g in air and 30 g in a liquid of density $1.24\times {10}^{3}kg/m^3$ kept at ${27}^{\circ }C$. When the temperature of the liquid is raised to ${42}^{\circ }C$, the metal piece weighs 30.5 g. The density of the liquid at ${42}^{\circ }C$ is $1.20\times {10}^{3}kg/m^3$. Calculate the coefficient of linear expansion of the metal.

1. 2.3 × 10⁶/°C

2. 1.2 × 10^-5/°C

3. 1.2 × 10⁵/°C

4. 2.3 × 10^-5/°C

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.

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. An ice block of mass 450 g has a volume of 500 cc. If the density of water is 1 g/cc, calculate the minimum force required to fully immerse the ice block.

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. $200c{m}^3$

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

Q.

A flask of volume $V$ contains some mercury. It is found that at different temperatures, the volume of air inside the flask remains the same. If ${\gamma }_g$ and ${\gamma }_m$ are the coefficients of cubical expansion of glass and mercury respectively, the volume of mercury in the flask is

1. $\frac{{\gamma }_{m}V}{{\gamma }_g}$

2. $\frac{{\gamma }_{g}V}{{\gamma }_m}$

3. $(1-\frac{{\gamma }_g}{{\gamma }_m})V$

4. $(1-\frac{{\gamma }_m}{{\gamma }_g})V$

Q.

Expansion during heating:

1. Occurs only in solids

2. Increases the weight of a material

3. Decreases the density of a material

4. Occurs at the same rate for all liquids and solids

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

1. $0.378J{g}^{-1}{K}^{-1}$
2. $0.578J{g}^{-1}{K}^{-1}$
3. $0.778J{g}^{-1}{K}^{-1}$
4. None of the above
   

Q.

The density of a liquid of coefficient of cubical expansion $\gamma$ is $\rho$ at $0^{\circ }C$. When the liquid is heated to a temperature T, the change in density will be

1. $\frac{-\rho \gamma T}{(1+\gamma T)}$

2. $\frac{\rho \gamma T}{(1+\gamma T)}$

3. $\frac{\rho (1+\gamma T)}{\gamma T}$

4. $-\frac{\rho (1+\gamma T)}{\gamma T}$

Q. Active mass of $0.64gS{O}_2$ In 10 lit vessel is:

1. $1\times {10}^{-2}M$
2. $1\times {10}^{-3}M$
3. $1\times {10}^{-1}M$
4. $0.64g$