 JEE Mains Previous Years Questions with Solutions

4.5
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1

AIEEE 2002

Two spheres of the same material have radii $1$ $m$ and $4$ $m$ and temperatures $4000$ $K$ and $2000$ $K$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is
A
$1:1$
B
$16:1$
C
$4:1$
D
$1:9$

Explanation

The energy radiated per second is given by $E = e\sigma {T^4}A$
For same material $e$ is same. $\sigma$ is stefan's constant
$\therefore$ ${{{E_1}} \over {{E_2}}} = {{T_1^4{A_1}} \over {T_2^4{A_2}}} = {{T_1^44\pi r_1^2} \over {T_2^44\pi r_2^2}}$
$= {{{{\left( {4000} \right)}^4} \times {1^2}} \over {{{\left( {2000} \right)}^4} \times {4^2}}} = {1 \over 1}$
2

AIEEE 2002

At what temperature is the $r.m.s$ velocity of a hydrogen molecule equal to that of an oxygen molecule at ${47^ \circ }C?$
A
$80K$
B
$-73$ $K$
C
$3$ $K$
D
$20$ $K$

Explanation

${v_{rms}} =$$\sqrt {{{RT} \over M}}$

For ${v_{rms}}$ to be equal ${{{T_{{H_2}}}} \over {{M_{{H_2}}}}} = {{{T_{{O_2}}}} \over {{M_{{O_2}}}}}$

Here ${M_{{H_2}}} = 2;\,\,{M_{{O_2}}} = 32;$

${T_{{O_2}}} = 47 + 273 = 320K$

$\therefore$ ${{{T_{{H_2}}}} \over 2} = {{320} \over {32}}$

$\Rightarrow {T_{{H_2}}} = 20K$
3

AIEEE 2002

Even Carnot engine cannot give $100\%$ efficiency because we cannot
A
B
find ideal sources
C
reach absolute zero temperature
D
eliminate friction.

Explanation

$\eta = 1 - {{{T_2}} \over {{T_1}}}$
For $\eta = 1$ or $100\%$, ${T_2} = 0K.$
The temperature of $0$ $K$ (absolute zero) can not be obtained.
4

AIEEE 2002

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will
A
increase
B
decrease
C
remain same
D
decrease for some, while increase for others

Explanation

Since pressure and volume are not changing, so temperature remains same.