1
AIEEE 2007
+4
-1
One end of a thermally insulated rod is kept at a temperature $${T_1}$$ and the other at $${T_2}$$. The rod is composed of two sections of length $${L_1}$$ and $${L_2}$$ and thermal conductivities $${K_1}$$ and $${K_2}$$ respectively. The temperature at the interface of the two section is
A
$${{\left( {{K_1}{L_1}{T_1} + {K_2}{L_2}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}$$
B
$${{\left( {{K_2}{L_2}{T_1} + {K_1}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}$$
C
$${{\left( {{K_2}{L_1}{T_1} + {K_1}{L_2}{T_2}} \right)} \over {\left( {{K_2}{L_1} + {K_1}{L_2}} \right)}}$$
D
$${{\left( {{K_1}{L_2}{T_1} + {K_2}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_2} + {K_2}{L_1}} \right)}}$$
2
AIEEE 2006
+4
-1
The work of $$146$$ $$kJ$$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $${7^ \circ }C.$$ The gas is $$\left( {R = 8.3J\,\,mo{l^{ - 1}}\,{K^{ - 1}}} \right)$$
A
diatomic
B
triatomic
C
a mixture of monoatomic and diatomic
D
monoatomic
3
AIEEE 2006
+4
-1
Assuming the Sun to be a spherical body of radius $$R$$ at a temperature of $$TK$$, evaluate the total radiant powered incident of Earth at a distance $$r$$ from the Sun

Where r0 is the radius of the Earth and $$\sigma$$ is Stefan's constant.

A
$$4\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}$$
B
$$\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}$$
C
$$r_0^2{R^2}\sigma {{{T^4}} \over {4\pi {r^2}}}$$
D
$${R^2}\sigma {{{T^4}} \over {{r^2}}}$$
4
AIEEE 2006
+4
-1
Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $${T_0},$$ while Box contains one mole of helium at temperature $$\left( {{7 \over 3}} \right){T_0}.$$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, $${T_f}$$ in terms of $${T_0}$$ is
A
$${T_f} = {3 \over 7}{T_0}$$
B
$${T_f} = {7 \over 3}{T_0}$$
C
$${T_f} = {3 \over 2}{T_0}$$
D
$${T_f} = {5 \over 2}{T_0}$$
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