01. Thermal Expansion (Linear, Area and Volume Expansion)
Thermal Properties of Matter

146632 An air bubble of volume ' $V_{1}$ ' is at the bottom of a lake of depth ' $d$ ', where the temperature is $T_{1}$. The bubble rises to the surface, which is at a temperature of $T_{2}$. Assuming that the bubble's air is at the same temperature as that of surrounding water, the volume of the bubble at the surface is (Let $P_{0}$ is the atmospheric pressure and $P_{1}$ is the pressure at $T_{1}$ )

1 $\frac{\mathrm{nRT}_{2}}{\mathrm{P}_{1}}$
2 $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}\left(\frac{\mathrm{P}_{0}+\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
3 $\frac{\mathrm{nRT}_{1}}{\mathrm{P}_{1}}$
4 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\left(\frac{\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
Thermal Properties of Matter

146633 Two identical glass spheres filled with air are connected by a horizontal glass tube the glass tube contains a pellet of mercury at its midpoint. Air in one sphere is at $0^{\circ} \mathrm{C}$ and the other is at $20^{\circ} \mathrm{C}$. If both the vessels are heated through $10^{\circ} \mathrm{C}$, then neglecting the expansions of the bulbs and the tube

1 the mercury pellet gets displaced towards the sphere at lower temperature.
2 the mercury pellet gets displaced towards the sphere at higher temperature.
3 the mercury pellet does not get displaced at all.
4 the temperature rise cause the pellet to expand without any displacement.
Thermal Properties of Matter

146634 Resistance of the wire is measured as $2 \Omega$ and $3 \Omega$ at $10^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$ respectively. Temperature co-efficient of resistance of the material of the wire is:

1 $0.033^{\circ} \mathrm{C}^{-1}$
2 $-0.033^{\circ} \mathrm{C}^{-1}$
3 $0.011^{\circ} \mathrm{C}^{-1}$
4 $0.055^{\circ} \mathrm{C}^{-1}$
Thermal Properties of Matter

146635 The resistance of a copper conductor at $50^{\circ} \mathrm{C}$ and $75^{\circ} \mathrm{C}$ are respectively $2.4 \Omega$ and $2.6 \Omega$. Find the temperature coefficient of resistance of copper.

1 $4 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
2 $3.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
3 $4.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
4 $5 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
Thermal Properties of Matter

146636 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. Calculate the fractional change in its density for $3^{\circ} \mathrm{C}$ rise in its temperature.

1 $4.9 \times 10^{-2}$
2 $3.2 \times 10^{-2}$
3 $1.5 \times 10^{-2}$
4 $0.8 \times 10^{-2}$
Thermal Properties of Matter

146632 An air bubble of volume ' $V_{1}$ ' is at the bottom of a lake of depth ' $d$ ', where the temperature is $T_{1}$. The bubble rises to the surface, which is at a temperature of $T_{2}$. Assuming that the bubble's air is at the same temperature as that of surrounding water, the volume of the bubble at the surface is (Let $P_{0}$ is the atmospheric pressure and $P_{1}$ is the pressure at $T_{1}$ )

1 $\frac{\mathrm{nRT}_{2}}{\mathrm{P}_{1}}$
2 $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}\left(\frac{\mathrm{P}_{0}+\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
3 $\frac{\mathrm{nRT}_{1}}{\mathrm{P}_{1}}$
4 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\left(\frac{\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
Thermal Properties of Matter

146633 Two identical glass spheres filled with air are connected by a horizontal glass tube the glass tube contains a pellet of mercury at its midpoint. Air in one sphere is at $0^{\circ} \mathrm{C}$ and the other is at $20^{\circ} \mathrm{C}$. If both the vessels are heated through $10^{\circ} \mathrm{C}$, then neglecting the expansions of the bulbs and the tube

1 the mercury pellet gets displaced towards the sphere at lower temperature.
2 the mercury pellet gets displaced towards the sphere at higher temperature.
3 the mercury pellet does not get displaced at all.
4 the temperature rise cause the pellet to expand without any displacement.
Thermal Properties of Matter

146634 Resistance of the wire is measured as $2 \Omega$ and $3 \Omega$ at $10^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$ respectively. Temperature co-efficient of resistance of the material of the wire is:

1 $0.033^{\circ} \mathrm{C}^{-1}$
2 $-0.033^{\circ} \mathrm{C}^{-1}$
3 $0.011^{\circ} \mathrm{C}^{-1}$
4 $0.055^{\circ} \mathrm{C}^{-1}$
Thermal Properties of Matter

146635 The resistance of a copper conductor at $50^{\circ} \mathrm{C}$ and $75^{\circ} \mathrm{C}$ are respectively $2.4 \Omega$ and $2.6 \Omega$. Find the temperature coefficient of resistance of copper.

1 $4 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
2 $3.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
3 $4.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
4 $5 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
Thermal Properties of Matter

146636 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. Calculate the fractional change in its density for $3^{\circ} \mathrm{C}$ rise in its temperature.

1 $4.9 \times 10^{-2}$
2 $3.2 \times 10^{-2}$
3 $1.5 \times 10^{-2}$
4 $0.8 \times 10^{-2}$
Thermal Properties of Matter

146632 An air bubble of volume ' $V_{1}$ ' is at the bottom of a lake of depth ' $d$ ', where the temperature is $T_{1}$. The bubble rises to the surface, which is at a temperature of $T_{2}$. Assuming that the bubble's air is at the same temperature as that of surrounding water, the volume of the bubble at the surface is (Let $P_{0}$ is the atmospheric pressure and $P_{1}$ is the pressure at $T_{1}$ )

1 $\frac{\mathrm{nRT}_{2}}{\mathrm{P}_{1}}$
2 $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}\left(\frac{\mathrm{P}_{0}+\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
3 $\frac{\mathrm{nRT}_{1}}{\mathrm{P}_{1}}$
4 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\left(\frac{\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
Thermal Properties of Matter

146633 Two identical glass spheres filled with air are connected by a horizontal glass tube the glass tube contains a pellet of mercury at its midpoint. Air in one sphere is at $0^{\circ} \mathrm{C}$ and the other is at $20^{\circ} \mathrm{C}$. If both the vessels are heated through $10^{\circ} \mathrm{C}$, then neglecting the expansions of the bulbs and the tube

1 the mercury pellet gets displaced towards the sphere at lower temperature.
2 the mercury pellet gets displaced towards the sphere at higher temperature.
3 the mercury pellet does not get displaced at all.
4 the temperature rise cause the pellet to expand without any displacement.
Thermal Properties of Matter

146634 Resistance of the wire is measured as $2 \Omega$ and $3 \Omega$ at $10^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$ respectively. Temperature co-efficient of resistance of the material of the wire is:

1 $0.033^{\circ} \mathrm{C}^{-1}$
2 $-0.033^{\circ} \mathrm{C}^{-1}$
3 $0.011^{\circ} \mathrm{C}^{-1}$
4 $0.055^{\circ} \mathrm{C}^{-1}$
Thermal Properties of Matter

146635 The resistance of a copper conductor at $50^{\circ} \mathrm{C}$ and $75^{\circ} \mathrm{C}$ are respectively $2.4 \Omega$ and $2.6 \Omega$. Find the temperature coefficient of resistance of copper.

1 $4 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
2 $3.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
3 $4.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
4 $5 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
Thermal Properties of Matter

146636 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. Calculate the fractional change in its density for $3^{\circ} \mathrm{C}$ rise in its temperature.

1 $4.9 \times 10^{-2}$
2 $3.2 \times 10^{-2}$
3 $1.5 \times 10^{-2}$
4 $0.8 \times 10^{-2}$
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Thermal Properties of Matter

146632 An air bubble of volume ' $V_{1}$ ' is at the bottom of a lake of depth ' $d$ ', where the temperature is $T_{1}$. The bubble rises to the surface, which is at a temperature of $T_{2}$. Assuming that the bubble's air is at the same temperature as that of surrounding water, the volume of the bubble at the surface is (Let $P_{0}$ is the atmospheric pressure and $P_{1}$ is the pressure at $T_{1}$ )

1 $\frac{\mathrm{nRT}_{2}}{\mathrm{P}_{1}}$
2 $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}\left(\frac{\mathrm{P}_{0}+\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
3 $\frac{\mathrm{nRT}_{1}}{\mathrm{P}_{1}}$
4 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\left(\frac{\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
Thermal Properties of Matter

146633 Two identical glass spheres filled with air are connected by a horizontal glass tube the glass tube contains a pellet of mercury at its midpoint. Air in one sphere is at $0^{\circ} \mathrm{C}$ and the other is at $20^{\circ} \mathrm{C}$. If both the vessels are heated through $10^{\circ} \mathrm{C}$, then neglecting the expansions of the bulbs and the tube

1 the mercury pellet gets displaced towards the sphere at lower temperature.
2 the mercury pellet gets displaced towards the sphere at higher temperature.
3 the mercury pellet does not get displaced at all.
4 the temperature rise cause the pellet to expand without any displacement.
Thermal Properties of Matter

146634 Resistance of the wire is measured as $2 \Omega$ and $3 \Omega$ at $10^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$ respectively. Temperature co-efficient of resistance of the material of the wire is:

1 $0.033^{\circ} \mathrm{C}^{-1}$
2 $-0.033^{\circ} \mathrm{C}^{-1}$
3 $0.011^{\circ} \mathrm{C}^{-1}$
4 $0.055^{\circ} \mathrm{C}^{-1}$
Thermal Properties of Matter

146635 The resistance of a copper conductor at $50^{\circ} \mathrm{C}$ and $75^{\circ} \mathrm{C}$ are respectively $2.4 \Omega$ and $2.6 \Omega$. Find the temperature coefficient of resistance of copper.

1 $4 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
2 $3.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
3 $4.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
4 $5 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
Thermal Properties of Matter

146636 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. Calculate the fractional change in its density for $3^{\circ} \mathrm{C}$ rise in its temperature.

1 $4.9 \times 10^{-2}$
2 $3.2 \times 10^{-2}$
3 $1.5 \times 10^{-2}$
4 $0.8 \times 10^{-2}$
Thermal Properties of Matter

146632 An air bubble of volume ' $V_{1}$ ' is at the bottom of a lake of depth ' $d$ ', where the temperature is $T_{1}$. The bubble rises to the surface, which is at a temperature of $T_{2}$. Assuming that the bubble's air is at the same temperature as that of surrounding water, the volume of the bubble at the surface is (Let $P_{0}$ is the atmospheric pressure and $P_{1}$ is the pressure at $T_{1}$ )

1 $\frac{\mathrm{nRT}_{2}}{\mathrm{P}_{1}}$
2 $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}\left(\frac{\mathrm{P}_{0}+\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
3 $\frac{\mathrm{nRT}_{1}}{\mathrm{P}_{1}}$
4 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\left(\frac{\rho g \mathrm{~d}}{\mathrm{P}_{0}}\right) \mathrm{V}_{1}$
Thermal Properties of Matter

146633 Two identical glass spheres filled with air are connected by a horizontal glass tube the glass tube contains a pellet of mercury at its midpoint. Air in one sphere is at $0^{\circ} \mathrm{C}$ and the other is at $20^{\circ} \mathrm{C}$. If both the vessels are heated through $10^{\circ} \mathrm{C}$, then neglecting the expansions of the bulbs and the tube

1 the mercury pellet gets displaced towards the sphere at lower temperature.
2 the mercury pellet gets displaced towards the sphere at higher temperature.
3 the mercury pellet does not get displaced at all.
4 the temperature rise cause the pellet to expand without any displacement.
Thermal Properties of Matter

146634 Resistance of the wire is measured as $2 \Omega$ and $3 \Omega$ at $10^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$ respectively. Temperature co-efficient of resistance of the material of the wire is:

1 $0.033^{\circ} \mathrm{C}^{-1}$
2 $-0.033^{\circ} \mathrm{C}^{-1}$
3 $0.011^{\circ} \mathrm{C}^{-1}$
4 $0.055^{\circ} \mathrm{C}^{-1}$
Thermal Properties of Matter

146635 The resistance of a copper conductor at $50^{\circ} \mathrm{C}$ and $75^{\circ} \mathrm{C}$ are respectively $2.4 \Omega$ and $2.6 \Omega$. Find the temperature coefficient of resistance of copper.

1 $4 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
2 $3.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
3 $4.8 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
4 $5 \times 10^{-3}{ }^{0} \mathrm{C}^{-1}$
Thermal Properties of Matter

146636 The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \mathrm{~K}^{-1}$. Calculate the fractional change in its density for $3^{\circ} \mathrm{C}$ rise in its temperature.

1 $4.9 \times 10^{-2}$
2 $3.2 \times 10^{-2}$
3 $1.5 \times 10^{-2}$
4 $0.8 \times 10^{-2}$