366824
A solid cube is first floating in a liquid. The coefficient of linear expansion of cube is \(\alpha\) and the coefficient of volume expansion of liquid is \(\gamma\). On increasing the temperature of (liquid + cube) system, the cube will sink if
1 \(\gamma=3 \alpha\)
2 \(\gamma>3 \alpha\)
3 \(\gamma < 3 \alpha\)
4 \(\gamma=2 \alpha\)
Explanation:
If \(\gamma>3 \alpha\) then for a same temperature rise the liquid expands more than solid and the liquid density decreases. So the cube should submerge more to balance its weight
PHXI11:THERMAL PROPERTIES OF MATTER
366825
Real expansion of liquid is
1 Independent on expansion of the vessel.
2 Dependent on expansion of the vessel.
3 Independent on nature of the liquid.
4 Depends on both nature of the liquid and vessel.
Explanation:
Conceptual Question
PHXI11:THERMAL PROPERTIES OF MATTER
366826
A beaker is completely filled with water at \(4^\circ C\). It will overflow if
1 Both heated and cooled above and below \(4^\circ C\) respectively
2 Heated above \(4^\circ C.\)
3 Cooled below \(4^\circ C.\)
4 None of these
Explanation:
Water has maximum density at \(4^\circ C\), so if the water is heated above \(4^\circ C\) density decreases, i.e., volume increases. In other words, it expands so it overflows in both the cases.
PHXI11:THERMAL PROPERTIES OF MATTER
366827
The coefficient of volume expansion of a liquid is \(49 \times {10^{ - 5}}\;{K^{ - 1}}\). Calculate the fractional change in its density when the temperature is raised by \(30^\circ C.\)
1 \(3.0 \times 10^{-2}\)
2 \(7.5 \times 10^{-2}\)
3 \(1.1 \times 10^{-2}\)
4 \(1.5 \times 10^{-2}\)
Explanation:
When the temperature of a liquid is increased by \(\Delta T^{\circ} \mathrm{C}\) the mass will remain unchanged while due to thermal expansion volume will increase and becomes \(V^{\prime}\). \(V^{\prime}=V(1+\gamma \Delta T)\) where \(\gamma\) is the coefficient of volume expansion of liquid \(\therefore \quad \rho^{\prime}=\dfrac{m}{V^{\prime}}=\dfrac{m}{V(1+\gamma \Delta T)}=\dfrac{\rho}{1+\gamma \Delta T}\) Fractional change in density \(=\dfrac{\rho-\rho^{\prime}}{\rho}\) \(\begin{aligned}& =\left(1-\dfrac{\rho^{\prime}}{\rho}\right)=\left(1-\dfrac{1}{1+\gamma \Delta T}\right) \\& =\dfrac{\gamma \Delta T}{1+\gamma \Delta T}=\dfrac{49 \times 10^{-5} \times 30}{1+49 \times 10^{-5} \times 30} \\& =\dfrac{0.0147}{1.0147}=0.0145 \approx 1.5 \times 10^{-2}\end{aligned}\)
366824
A solid cube is first floating in a liquid. The coefficient of linear expansion of cube is \(\alpha\) and the coefficient of volume expansion of liquid is \(\gamma\). On increasing the temperature of (liquid + cube) system, the cube will sink if
1 \(\gamma=3 \alpha\)
2 \(\gamma>3 \alpha\)
3 \(\gamma < 3 \alpha\)
4 \(\gamma=2 \alpha\)
Explanation:
If \(\gamma>3 \alpha\) then for a same temperature rise the liquid expands more than solid and the liquid density decreases. So the cube should submerge more to balance its weight
PHXI11:THERMAL PROPERTIES OF MATTER
366825
Real expansion of liquid is
1 Independent on expansion of the vessel.
2 Dependent on expansion of the vessel.
3 Independent on nature of the liquid.
4 Depends on both nature of the liquid and vessel.
Explanation:
Conceptual Question
PHXI11:THERMAL PROPERTIES OF MATTER
366826
A beaker is completely filled with water at \(4^\circ C\). It will overflow if
1 Both heated and cooled above and below \(4^\circ C\) respectively
2 Heated above \(4^\circ C.\)
3 Cooled below \(4^\circ C.\)
4 None of these
Explanation:
Water has maximum density at \(4^\circ C\), so if the water is heated above \(4^\circ C\) density decreases, i.e., volume increases. In other words, it expands so it overflows in both the cases.
PHXI11:THERMAL PROPERTIES OF MATTER
366827
The coefficient of volume expansion of a liquid is \(49 \times {10^{ - 5}}\;{K^{ - 1}}\). Calculate the fractional change in its density when the temperature is raised by \(30^\circ C.\)
1 \(3.0 \times 10^{-2}\)
2 \(7.5 \times 10^{-2}\)
3 \(1.1 \times 10^{-2}\)
4 \(1.5 \times 10^{-2}\)
Explanation:
When the temperature of a liquid is increased by \(\Delta T^{\circ} \mathrm{C}\) the mass will remain unchanged while due to thermal expansion volume will increase and becomes \(V^{\prime}\). \(V^{\prime}=V(1+\gamma \Delta T)\) where \(\gamma\) is the coefficient of volume expansion of liquid \(\therefore \quad \rho^{\prime}=\dfrac{m}{V^{\prime}}=\dfrac{m}{V(1+\gamma \Delta T)}=\dfrac{\rho}{1+\gamma \Delta T}\) Fractional change in density \(=\dfrac{\rho-\rho^{\prime}}{\rho}\) \(\begin{aligned}& =\left(1-\dfrac{\rho^{\prime}}{\rho}\right)=\left(1-\dfrac{1}{1+\gamma \Delta T}\right) \\& =\dfrac{\gamma \Delta T}{1+\gamma \Delta T}=\dfrac{49 \times 10^{-5} \times 30}{1+49 \times 10^{-5} \times 30} \\& =\dfrac{0.0147}{1.0147}=0.0145 \approx 1.5 \times 10^{-2}\end{aligned}\)
366824
A solid cube is first floating in a liquid. The coefficient of linear expansion of cube is \(\alpha\) and the coefficient of volume expansion of liquid is \(\gamma\). On increasing the temperature of (liquid + cube) system, the cube will sink if
1 \(\gamma=3 \alpha\)
2 \(\gamma>3 \alpha\)
3 \(\gamma < 3 \alpha\)
4 \(\gamma=2 \alpha\)
Explanation:
If \(\gamma>3 \alpha\) then for a same temperature rise the liquid expands more than solid and the liquid density decreases. So the cube should submerge more to balance its weight
PHXI11:THERMAL PROPERTIES OF MATTER
366825
Real expansion of liquid is
1 Independent on expansion of the vessel.
2 Dependent on expansion of the vessel.
3 Independent on nature of the liquid.
4 Depends on both nature of the liquid and vessel.
Explanation:
Conceptual Question
PHXI11:THERMAL PROPERTIES OF MATTER
366826
A beaker is completely filled with water at \(4^\circ C\). It will overflow if
1 Both heated and cooled above and below \(4^\circ C\) respectively
2 Heated above \(4^\circ C.\)
3 Cooled below \(4^\circ C.\)
4 None of these
Explanation:
Water has maximum density at \(4^\circ C\), so if the water is heated above \(4^\circ C\) density decreases, i.e., volume increases. In other words, it expands so it overflows in both the cases.
PHXI11:THERMAL PROPERTIES OF MATTER
366827
The coefficient of volume expansion of a liquid is \(49 \times {10^{ - 5}}\;{K^{ - 1}}\). Calculate the fractional change in its density when the temperature is raised by \(30^\circ C.\)
1 \(3.0 \times 10^{-2}\)
2 \(7.5 \times 10^{-2}\)
3 \(1.1 \times 10^{-2}\)
4 \(1.5 \times 10^{-2}\)
Explanation:
When the temperature of a liquid is increased by \(\Delta T^{\circ} \mathrm{C}\) the mass will remain unchanged while due to thermal expansion volume will increase and becomes \(V^{\prime}\). \(V^{\prime}=V(1+\gamma \Delta T)\) where \(\gamma\) is the coefficient of volume expansion of liquid \(\therefore \quad \rho^{\prime}=\dfrac{m}{V^{\prime}}=\dfrac{m}{V(1+\gamma \Delta T)}=\dfrac{\rho}{1+\gamma \Delta T}\) Fractional change in density \(=\dfrac{\rho-\rho^{\prime}}{\rho}\) \(\begin{aligned}& =\left(1-\dfrac{\rho^{\prime}}{\rho}\right)=\left(1-\dfrac{1}{1+\gamma \Delta T}\right) \\& =\dfrac{\gamma \Delta T}{1+\gamma \Delta T}=\dfrac{49 \times 10^{-5} \times 30}{1+49 \times 10^{-5} \times 30} \\& =\dfrac{0.0147}{1.0147}=0.0145 \approx 1.5 \times 10^{-2}\end{aligned}\)
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PHXI11:THERMAL PROPERTIES OF MATTER
366824
A solid cube is first floating in a liquid. The coefficient of linear expansion of cube is \(\alpha\) and the coefficient of volume expansion of liquid is \(\gamma\). On increasing the temperature of (liquid + cube) system, the cube will sink if
1 \(\gamma=3 \alpha\)
2 \(\gamma>3 \alpha\)
3 \(\gamma < 3 \alpha\)
4 \(\gamma=2 \alpha\)
Explanation:
If \(\gamma>3 \alpha\) then for a same temperature rise the liquid expands more than solid and the liquid density decreases. So the cube should submerge more to balance its weight
PHXI11:THERMAL PROPERTIES OF MATTER
366825
Real expansion of liquid is
1 Independent on expansion of the vessel.
2 Dependent on expansion of the vessel.
3 Independent on nature of the liquid.
4 Depends on both nature of the liquid and vessel.
Explanation:
Conceptual Question
PHXI11:THERMAL PROPERTIES OF MATTER
366826
A beaker is completely filled with water at \(4^\circ C\). It will overflow if
1 Both heated and cooled above and below \(4^\circ C\) respectively
2 Heated above \(4^\circ C.\)
3 Cooled below \(4^\circ C.\)
4 None of these
Explanation:
Water has maximum density at \(4^\circ C\), so if the water is heated above \(4^\circ C\) density decreases, i.e., volume increases. In other words, it expands so it overflows in both the cases.
PHXI11:THERMAL PROPERTIES OF MATTER
366827
The coefficient of volume expansion of a liquid is \(49 \times {10^{ - 5}}\;{K^{ - 1}}\). Calculate the fractional change in its density when the temperature is raised by \(30^\circ C.\)
1 \(3.0 \times 10^{-2}\)
2 \(7.5 \times 10^{-2}\)
3 \(1.1 \times 10^{-2}\)
4 \(1.5 \times 10^{-2}\)
Explanation:
When the temperature of a liquid is increased by \(\Delta T^{\circ} \mathrm{C}\) the mass will remain unchanged while due to thermal expansion volume will increase and becomes \(V^{\prime}\). \(V^{\prime}=V(1+\gamma \Delta T)\) where \(\gamma\) is the coefficient of volume expansion of liquid \(\therefore \quad \rho^{\prime}=\dfrac{m}{V^{\prime}}=\dfrac{m}{V(1+\gamma \Delta T)}=\dfrac{\rho}{1+\gamma \Delta T}\) Fractional change in density \(=\dfrac{\rho-\rho^{\prime}}{\rho}\) \(\begin{aligned}& =\left(1-\dfrac{\rho^{\prime}}{\rho}\right)=\left(1-\dfrac{1}{1+\gamma \Delta T}\right) \\& =\dfrac{\gamma \Delta T}{1+\gamma \Delta T}=\dfrac{49 \times 10^{-5} \times 30}{1+49 \times 10^{-5} \times 30} \\& =\dfrac{0.0147}{1.0147}=0.0145 \approx 1.5 \times 10^{-2}\end{aligned}\)
