Thermal Expansion
PHXI11:THERMAL PROPERTIES OF MATTER

366686 The radius of a metal sphere at room temperature \(T\) is \(R\), and the coefficient of linear expansion of the metal is \(\alpha\). The sphere is heated a little by a temperature \(\Delta T\) so that its new temperature is \(T+\Delta T\). The increase in the volume of the sphere is approximiately

1 \(2 \pi R \alpha \Delta T\)
2 \(\pi R^{2} \alpha \Delta T\)
3 \(4 \pi R^{2} \alpha \Delta T / 3\)
4 \(4 \pi R^{3} \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366687 An external pressure \(P\) is applied on a cube at \(0^\circ C\) so that it is equally compressed from all sides. \(K\) is the bulk modulus of the material of the cube and \(\alpha\) is its coefficient of linear expansion. Suppose we want to bring the cube to its original size of heating. The temperature should be raised by:

1 \(\dfrac{3 \alpha}{P K}\)
2 \(3 P K \alpha\)
3 \(\dfrac{P}{3 \alpha K}\)
4 \(\dfrac{P}{\alpha K}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366688 The coefficient of linear expansion of a metal is \(1 \times {10^{ - 5}}/^\circ C\). The percentage increase in area of a square plate of that metal when it is heated through \(100^\circ C\) is

1 \(0.02 \%\)
2 \(0.1 \%\)
3 \(0.001 \%\)
4 \(0.2 \%\)
PHXI11:THERMAL PROPERTIES OF MATTER

366689 A crystal has a coefficient of expansion \(13 \times 10^{-7}\) in one direction and \(231 \times 10^{-7}\) in every direction at right angles to it. Then the cubical coefficient of expansion is

1 \(244 \times 10^{-7}\)
2 \(462 \times 10^{-7}\)
3 \(257 \times 10^{-7}\)
4 \(475 \times 10^{-7}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366690 If the length of a cylinder on heating increases by \(2 \%\), the area of its base will increase by

1 \(4 \%\)
2 \(2 \%\)
3 \(1 \%\)
4 \(0.5 \%\)
PHXI11:THERMAL PROPERTIES OF MATTER

366686 The radius of a metal sphere at room temperature \(T\) is \(R\), and the coefficient of linear expansion of the metal is \(\alpha\). The sphere is heated a little by a temperature \(\Delta T\) so that its new temperature is \(T+\Delta T\). The increase in the volume of the sphere is approximiately

1 \(2 \pi R \alpha \Delta T\)
2 \(\pi R^{2} \alpha \Delta T\)
3 \(4 \pi R^{2} \alpha \Delta T / 3\)
4 \(4 \pi R^{3} \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366687 An external pressure \(P\) is applied on a cube at \(0^\circ C\) so that it is equally compressed from all sides. \(K\) is the bulk modulus of the material of the cube and \(\alpha\) is its coefficient of linear expansion. Suppose we want to bring the cube to its original size of heating. The temperature should be raised by:

1 \(\dfrac{3 \alpha}{P K}\)
2 \(3 P K \alpha\)
3 \(\dfrac{P}{3 \alpha K}\)
4 \(\dfrac{P}{\alpha K}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366688 The coefficient of linear expansion of a metal is \(1 \times {10^{ - 5}}/^\circ C\). The percentage increase in area of a square plate of that metal when it is heated through \(100^\circ C\) is

1 \(0.02 \%\)
2 \(0.1 \%\)
3 \(0.001 \%\)
4 \(0.2 \%\)
PHXI11:THERMAL PROPERTIES OF MATTER

366689 A crystal has a coefficient of expansion \(13 \times 10^{-7}\) in one direction and \(231 \times 10^{-7}\) in every direction at right angles to it. Then the cubical coefficient of expansion is

1 \(244 \times 10^{-7}\)
2 \(462 \times 10^{-7}\)
3 \(257 \times 10^{-7}\)
4 \(475 \times 10^{-7}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366690 If the length of a cylinder on heating increases by \(2 \%\), the area of its base will increase by

1 \(4 \%\)
2 \(2 \%\)
3 \(1 \%\)
4 \(0.5 \%\)
PHXI11:THERMAL PROPERTIES OF MATTER

366686 The radius of a metal sphere at room temperature \(T\) is \(R\), and the coefficient of linear expansion of the metal is \(\alpha\). The sphere is heated a little by a temperature \(\Delta T\) so that its new temperature is \(T+\Delta T\). The increase in the volume of the sphere is approximiately

1 \(2 \pi R \alpha \Delta T\)
2 \(\pi R^{2} \alpha \Delta T\)
3 \(4 \pi R^{2} \alpha \Delta T / 3\)
4 \(4 \pi R^{3} \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366687 An external pressure \(P\) is applied on a cube at \(0^\circ C\) so that it is equally compressed from all sides. \(K\) is the bulk modulus of the material of the cube and \(\alpha\) is its coefficient of linear expansion. Suppose we want to bring the cube to its original size of heating. The temperature should be raised by:

1 \(\dfrac{3 \alpha}{P K}\)
2 \(3 P K \alpha\)
3 \(\dfrac{P}{3 \alpha K}\)
4 \(\dfrac{P}{\alpha K}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366688 The coefficient of linear expansion of a metal is \(1 \times {10^{ - 5}}/^\circ C\). The percentage increase in area of a square plate of that metal when it is heated through \(100^\circ C\) is

1 \(0.02 \%\)
2 \(0.1 \%\)
3 \(0.001 \%\)
4 \(0.2 \%\)
PHXI11:THERMAL PROPERTIES OF MATTER

366689 A crystal has a coefficient of expansion \(13 \times 10^{-7}\) in one direction and \(231 \times 10^{-7}\) in every direction at right angles to it. Then the cubical coefficient of expansion is

1 \(244 \times 10^{-7}\)
2 \(462 \times 10^{-7}\)
3 \(257 \times 10^{-7}\)
4 \(475 \times 10^{-7}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366690 If the length of a cylinder on heating increases by \(2 \%\), the area of its base will increase by

1 \(4 \%\)
2 \(2 \%\)
3 \(1 \%\)
4 \(0.5 \%\)
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PHXI11:THERMAL PROPERTIES OF MATTER

366686 The radius of a metal sphere at room temperature \(T\) is \(R\), and the coefficient of linear expansion of the metal is \(\alpha\). The sphere is heated a little by a temperature \(\Delta T\) so that its new temperature is \(T+\Delta T\). The increase in the volume of the sphere is approximiately

1 \(2 \pi R \alpha \Delta T\)
2 \(\pi R^{2} \alpha \Delta T\)
3 \(4 \pi R^{2} \alpha \Delta T / 3\)
4 \(4 \pi R^{3} \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366687 An external pressure \(P\) is applied on a cube at \(0^\circ C\) so that it is equally compressed from all sides. \(K\) is the bulk modulus of the material of the cube and \(\alpha\) is its coefficient of linear expansion. Suppose we want to bring the cube to its original size of heating. The temperature should be raised by:

1 \(\dfrac{3 \alpha}{P K}\)
2 \(3 P K \alpha\)
3 \(\dfrac{P}{3 \alpha K}\)
4 \(\dfrac{P}{\alpha K}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366688 The coefficient of linear expansion of a metal is \(1 \times {10^{ - 5}}/^\circ C\). The percentage increase in area of a square plate of that metal when it is heated through \(100^\circ C\) is

1 \(0.02 \%\)
2 \(0.1 \%\)
3 \(0.001 \%\)
4 \(0.2 \%\)
PHXI11:THERMAL PROPERTIES OF MATTER

366689 A crystal has a coefficient of expansion \(13 \times 10^{-7}\) in one direction and \(231 \times 10^{-7}\) in every direction at right angles to it. Then the cubical coefficient of expansion is

1 \(244 \times 10^{-7}\)
2 \(462 \times 10^{-7}\)
3 \(257 \times 10^{-7}\)
4 \(475 \times 10^{-7}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366690 If the length of a cylinder on heating increases by \(2 \%\), the area of its base will increase by

1 \(4 \%\)
2 \(2 \%\)
3 \(1 \%\)
4 \(0.5 \%\)
PHXI11:THERMAL PROPERTIES OF MATTER

366686 The radius of a metal sphere at room temperature \(T\) is \(R\), and the coefficient of linear expansion of the metal is \(\alpha\). The sphere is heated a little by a temperature \(\Delta T\) so that its new temperature is \(T+\Delta T\). The increase in the volume of the sphere is approximiately

1 \(2 \pi R \alpha \Delta T\)
2 \(\pi R^{2} \alpha \Delta T\)
3 \(4 \pi R^{2} \alpha \Delta T / 3\)
4 \(4 \pi R^{3} \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366687 An external pressure \(P\) is applied on a cube at \(0^\circ C\) so that it is equally compressed from all sides. \(K\) is the bulk modulus of the material of the cube and \(\alpha\) is its coefficient of linear expansion. Suppose we want to bring the cube to its original size of heating. The temperature should be raised by:

1 \(\dfrac{3 \alpha}{P K}\)
2 \(3 P K \alpha\)
3 \(\dfrac{P}{3 \alpha K}\)
4 \(\dfrac{P}{\alpha K}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366688 The coefficient of linear expansion of a metal is \(1 \times {10^{ - 5}}/^\circ C\). The percentage increase in area of a square plate of that metal when it is heated through \(100^\circ C\) is

1 \(0.02 \%\)
2 \(0.1 \%\)
3 \(0.001 \%\)
4 \(0.2 \%\)
PHXI11:THERMAL PROPERTIES OF MATTER

366689 A crystal has a coefficient of expansion \(13 \times 10^{-7}\) in one direction and \(231 \times 10^{-7}\) in every direction at right angles to it. Then the cubical coefficient of expansion is

1 \(244 \times 10^{-7}\)
2 \(462 \times 10^{-7}\)
3 \(257 \times 10^{-7}\)
4 \(475 \times 10^{-7}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366690 If the length of a cylinder on heating increases by \(2 \%\), the area of its base will increase by

1 \(4 \%\)
2 \(2 \%\)
3 \(1 \%\)
4 \(0.5 \%\)