1
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

A small spherical monoatomic ideal gas bubble $$\left( {\gamma = {5 \over 3}} \right)$$ is trapped inside a liquid of density $$\rho_1$$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T$$_0$$, the height of the liquid is H and the atmospheric pressure is P$$_0$$ (Neglect surface tension)

IIT-JEE 2008 Paper 1 Offline Physics - Properties of Matter Question 5 English Comprehension

When the gas bubble is at a height y from the bottom, its temperature is :

A
$${T_0}{\left( {{{{P_0} + {\rho _l}gH} \over {{P_0} + {\rho _l}gy}}} \right)^{{2 \over 5}}}$$
B
$${T_0}{\left( {{{{P_0} + {\rho _l}g(H - y)} \over {{P_0} + {\rho _l}gH}}} \right)^{{2 \over 5}}}$$
C
$${T_0}{\left( {{{{P_0} + {\rho _l}gH} \over {{P_0} + {\rho _l}gy}}} \right)^{{3 \over 5}}}$$
D
$${T_0}{\left( {{{{P_0} + {\rho _l}g(H - y)} \over {{P_0} + {\rho _l}gH}}} \right)^{{3 \over 5}}}$$
2
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

A small spherical monoatomic ideal gas bubble $$\left( {\gamma = {5 \over 3}} \right)$$ is trapped inside a liquid of density $$\rho_1$$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T$$_0$$, the height of the liquid is H and the atmospheric pressure is P$$_0$$ (Neglect surface tension)

IIT-JEE 2008 Paper 1 Offline Physics - Properties of Matter Question 8 English Comprehension

The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

A
$${\rho _l}nRg{T_0}{{{{({P_0} + {\rho _l}gH)}^{{2 \over 5}}}} \over {{{({P_0} + {\rho _l}gy)}^{{7 \over 5}}}}}$$
B
$${{{\rho _l}nRg{T_0}} \over {{{({P_0} + {\rho _l}gH)}^{{2 \over 5}}}{{[{P_0} + {\rho _l}g(H - y)]}^{{3 \over 5}}}}}$$
C
$${\rho _l}nRg{T_0}{{{{({P_0} + {\rho _l}gH)}^{{3 \over 5}}}} \over {{{({P_0} + {\rho _l}gy)}^{{8 \over 5}}}}}$$
D
$${{{\rho _l}nRg{T_0}} \over {{{({P_0} + {\rho _l}gH)}^{{3 \over 5}}}[{P_0} + {\rho _l}g{{(H - y)}^{{2 \over 5}}}}}$$
3
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

In a mixture of H - He$$^+$$ gas (He$$^+$$ is singly ionized He atom), H atoms and He$$^+$$ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He$$^+$$ ions (by collisions). Assume that the Bohr model of atom is exactly valid.

The quantum number n of the state finally populated in He$$^+$$ ions is :

A
2
B
3
C
4
D
5
4
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

In a mixture of H - He$$^+$$ gas (He$$^+$$ is singly ionized He atom), H atoms and He$$^+$$ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He$$^+$$ ions (by collisions). Assume that the Bohr model of atom is exactly valid.

The wavelength of light emitted in the visible region by He$$^+$$ ions after collisions with H atoms is

A
$$6.5\times10^{-7}$$ m
B
$$5.6\times10^{-7}$$ m
C
$$4.8\times10^{-7}$$ m
D
$$4.0\times10^{-7}$$ m
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