Thermal Expansion
PHXI11:THERMAL PROPERTIES OF MATTER

366811 A steel rail of length \(5\;m\) and area of cross section \(40\;c{m^2}\) is prevented from expanding along its length while the temperature rises by \(10^\circ C\). If coefficient of linear expansion and young's modulus of steel are \(1.2 \times {10^{ - 5}}\;{K^{ - 1}}\) and \(2 \times {10^{11}}N{m^{ - 2}}\) respectively, the force developed in the rail is approxmately:

1 \(2 \times {10^7}\;N\)
2 \(2 \times {10^9}\;N\)
3 \(3 \times {10^{ - 5}}\;N\)
4 \(1 \times {10^5}\;N\)
PHXI11:THERMAL PROPERTIES OF MATTER

366812 Two rods of different metals having the same area of cross-section \(A\) are placed between the two massive walls as shown in figure. The first rod has a length \(l_{1}\), coefficient of linear expansion \(\alpha_{1}\) and Young's modulus \(Y_{1}\). The corresponding quantities for second rod are \(l_{2}, \alpha_{2}\) and \(Y_{2}\). The temperature of both the rods is now raised by \(\Delta T\). The displacement of the junction is
supporting img

1 \(l_{1} l_{2} \Delta T\)
2 \(\dfrac{l_{1} l_{2} \Delta T\left(Y_{1} \alpha_{1} \sim Y_{2} \alpha_{2}\right)}{Y_{1} l_{2}+Y_{2} l_{1}}\)
3 \(\dfrac{l_{1} l_{2} \Delta T\left(Y_{1} l_{2}+Y_{2} l_{1}\right)}{Y_{1} \alpha_{1}+Y_{2} \alpha_{2}}\)
4 \(\dfrac{l_{1} l_{2}\left(Y_{1} \alpha_{1}-Y_{2} \alpha_{2}\right) \Delta T}{Y_{1} l_{1}+Y_{2} l_{2}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366813 A metallic bar of Young's modulus, \({0.5 \times 10^{11} {Nm}^{-2}}\) and coefficient of linear thermal expansion \({10^{-5^{\circ}} {C}^{-1}}\), length 1 m and area of cross-section \({10^{-3} {~m}^{2}}\) is heated from \({0^{\circ} {C}}\) to \({100^{\circ} {C}}\) without expansion or bending. The compressive force developed in it is:

1 \({5 \times 10^{3} {~N}}\)
2 \({50 \times 10^{3} {~N}}\)
3 \({100 \times 10^{3} {~N}}\)
4 \({2 \times 10^{3} {~N}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366814 The coefficient of real expansion of mercury is \(0.18 \times {10^{ - 3}}{C^{\, - 1}}.\) If the density of mercury at \(0^\circ C\) is \(13.6\;g/cc,\) its density at \(473\;K\) will be

1 \(13.12\;g/cc\)
2 \(13.65\;g/cc\)
3 \(13.51\;g/cc\)
4 \(13.22\;g/cc\)
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PHXI11:THERMAL PROPERTIES OF MATTER

366811 A steel rail of length \(5\;m\) and area of cross section \(40\;c{m^2}\) is prevented from expanding along its length while the temperature rises by \(10^\circ C\). If coefficient of linear expansion and young's modulus of steel are \(1.2 \times {10^{ - 5}}\;{K^{ - 1}}\) and \(2 \times {10^{11}}N{m^{ - 2}}\) respectively, the force developed in the rail is approxmately:

1 \(2 \times {10^7}\;N\)
2 \(2 \times {10^9}\;N\)
3 \(3 \times {10^{ - 5}}\;N\)
4 \(1 \times {10^5}\;N\)
PHXI11:THERMAL PROPERTIES OF MATTER

366812 Two rods of different metals having the same area of cross-section \(A\) are placed between the two massive walls as shown in figure. The first rod has a length \(l_{1}\), coefficient of linear expansion \(\alpha_{1}\) and Young's modulus \(Y_{1}\). The corresponding quantities for second rod are \(l_{2}, \alpha_{2}\) and \(Y_{2}\). The temperature of both the rods is now raised by \(\Delta T\). The displacement of the junction is
supporting img

1 \(l_{1} l_{2} \Delta T\)
2 \(\dfrac{l_{1} l_{2} \Delta T\left(Y_{1} \alpha_{1} \sim Y_{2} \alpha_{2}\right)}{Y_{1} l_{2}+Y_{2} l_{1}}\)
3 \(\dfrac{l_{1} l_{2} \Delta T\left(Y_{1} l_{2}+Y_{2} l_{1}\right)}{Y_{1} \alpha_{1}+Y_{2} \alpha_{2}}\)
4 \(\dfrac{l_{1} l_{2}\left(Y_{1} \alpha_{1}-Y_{2} \alpha_{2}\right) \Delta T}{Y_{1} l_{1}+Y_{2} l_{2}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366813 A metallic bar of Young's modulus, \({0.5 \times 10^{11} {Nm}^{-2}}\) and coefficient of linear thermal expansion \({10^{-5^{\circ}} {C}^{-1}}\), length 1 m and area of cross-section \({10^{-3} {~m}^{2}}\) is heated from \({0^{\circ} {C}}\) to \({100^{\circ} {C}}\) without expansion or bending. The compressive force developed in it is:

1 \({5 \times 10^{3} {~N}}\)
2 \({50 \times 10^{3} {~N}}\)
3 \({100 \times 10^{3} {~N}}\)
4 \({2 \times 10^{3} {~N}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366814 The coefficient of real expansion of mercury is \(0.18 \times {10^{ - 3}}{C^{\, - 1}}.\) If the density of mercury at \(0^\circ C\) is \(13.6\;g/cc,\) its density at \(473\;K\) will be

1 \(13.12\;g/cc\)
2 \(13.65\;g/cc\)
3 \(13.51\;g/cc\)
4 \(13.22\;g/cc\)
PHXI11:THERMAL PROPERTIES OF MATTER

366811 A steel rail of length \(5\;m\) and area of cross section \(40\;c{m^2}\) is prevented from expanding along its length while the temperature rises by \(10^\circ C\). If coefficient of linear expansion and young's modulus of steel are \(1.2 \times {10^{ - 5}}\;{K^{ - 1}}\) and \(2 \times {10^{11}}N{m^{ - 2}}\) respectively, the force developed in the rail is approxmately:

1 \(2 \times {10^7}\;N\)
2 \(2 \times {10^9}\;N\)
3 \(3 \times {10^{ - 5}}\;N\)
4 \(1 \times {10^5}\;N\)
PHXI11:THERMAL PROPERTIES OF MATTER

366812 Two rods of different metals having the same area of cross-section \(A\) are placed between the two massive walls as shown in figure. The first rod has a length \(l_{1}\), coefficient of linear expansion \(\alpha_{1}\) and Young's modulus \(Y_{1}\). The corresponding quantities for second rod are \(l_{2}, \alpha_{2}\) and \(Y_{2}\). The temperature of both the rods is now raised by \(\Delta T\). The displacement of the junction is
supporting img

1 \(l_{1} l_{2} \Delta T\)
2 \(\dfrac{l_{1} l_{2} \Delta T\left(Y_{1} \alpha_{1} \sim Y_{2} \alpha_{2}\right)}{Y_{1} l_{2}+Y_{2} l_{1}}\)
3 \(\dfrac{l_{1} l_{2} \Delta T\left(Y_{1} l_{2}+Y_{2} l_{1}\right)}{Y_{1} \alpha_{1}+Y_{2} \alpha_{2}}\)
4 \(\dfrac{l_{1} l_{2}\left(Y_{1} \alpha_{1}-Y_{2} \alpha_{2}\right) \Delta T}{Y_{1} l_{1}+Y_{2} l_{2}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366813 A metallic bar of Young's modulus, \({0.5 \times 10^{11} {Nm}^{-2}}\) and coefficient of linear thermal expansion \({10^{-5^{\circ}} {C}^{-1}}\), length 1 m and area of cross-section \({10^{-3} {~m}^{2}}\) is heated from \({0^{\circ} {C}}\) to \({100^{\circ} {C}}\) without expansion or bending. The compressive force developed in it is:

1 \({5 \times 10^{3} {~N}}\)
2 \({50 \times 10^{3} {~N}}\)
3 \({100 \times 10^{3} {~N}}\)
4 \({2 \times 10^{3} {~N}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366814 The coefficient of real expansion of mercury is \(0.18 \times {10^{ - 3}}{C^{\, - 1}}.\) If the density of mercury at \(0^\circ C\) is \(13.6\;g/cc,\) its density at \(473\;K\) will be

1 \(13.12\;g/cc\)
2 \(13.65\;g/cc\)
3 \(13.51\;g/cc\)
4 \(13.22\;g/cc\)
PHXI11:THERMAL PROPERTIES OF MATTER

366811 A steel rail of length \(5\;m\) and area of cross section \(40\;c{m^2}\) is prevented from expanding along its length while the temperature rises by \(10^\circ C\). If coefficient of linear expansion and young's modulus of steel are \(1.2 \times {10^{ - 5}}\;{K^{ - 1}}\) and \(2 \times {10^{11}}N{m^{ - 2}}\) respectively, the force developed in the rail is approxmately:

1 \(2 \times {10^7}\;N\)
2 \(2 \times {10^9}\;N\)
3 \(3 \times {10^{ - 5}}\;N\)
4 \(1 \times {10^5}\;N\)
PHXI11:THERMAL PROPERTIES OF MATTER

366812 Two rods of different metals having the same area of cross-section \(A\) are placed between the two massive walls as shown in figure. The first rod has a length \(l_{1}\), coefficient of linear expansion \(\alpha_{1}\) and Young's modulus \(Y_{1}\). The corresponding quantities for second rod are \(l_{2}, \alpha_{2}\) and \(Y_{2}\). The temperature of both the rods is now raised by \(\Delta T\). The displacement of the junction is
supporting img

1 \(l_{1} l_{2} \Delta T\)
2 \(\dfrac{l_{1} l_{2} \Delta T\left(Y_{1} \alpha_{1} \sim Y_{2} \alpha_{2}\right)}{Y_{1} l_{2}+Y_{2} l_{1}}\)
3 \(\dfrac{l_{1} l_{2} \Delta T\left(Y_{1} l_{2}+Y_{2} l_{1}\right)}{Y_{1} \alpha_{1}+Y_{2} \alpha_{2}}\)
4 \(\dfrac{l_{1} l_{2}\left(Y_{1} \alpha_{1}-Y_{2} \alpha_{2}\right) \Delta T}{Y_{1} l_{1}+Y_{2} l_{2}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366813 A metallic bar of Young's modulus, \({0.5 \times 10^{11} {Nm}^{-2}}\) and coefficient of linear thermal expansion \({10^{-5^{\circ}} {C}^{-1}}\), length 1 m and area of cross-section \({10^{-3} {~m}^{2}}\) is heated from \({0^{\circ} {C}}\) to \({100^{\circ} {C}}\) without expansion or bending. The compressive force developed in it is:

1 \({5 \times 10^{3} {~N}}\)
2 \({50 \times 10^{3} {~N}}\)
3 \({100 \times 10^{3} {~N}}\)
4 \({2 \times 10^{3} {~N}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366814 The coefficient of real expansion of mercury is \(0.18 \times {10^{ - 3}}{C^{\, - 1}}.\) If the density of mercury at \(0^\circ C\) is \(13.6\;g/cc,\) its density at \(473\;K\) will be

1 \(13.12\;g/cc\)
2 \(13.65\;g/cc\)
3 \(13.51\;g/cc\)
4 \(13.22\;g/cc\)