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1

AIEEE 2004

MCQ (Single Correct Answer)
If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio of the radiant energy received on earth to what it was previously will be
A
$$32$$
B
$$16$$
C
$$4$$
D
$$64$$

Explanation

$$E = \sigma A{T^4};\,\,A \propto {R^2}$$
$$\therefore$$ $$E \propto {R^2}{T^4}$$
$$\therefore$$ $${{{E_2}} \over {{E_1}}} = {{R_2^2T_2^4} \over {R_1^2T_1^4}}$$
$$ \Rightarrow {{{E_2}} \over {{E_1}}}$$
$$ = {{{{\left( {2R} \right)}^2}{{\left( {2T} \right)}^4}} \over {{R^2}{T^4}}}$$
$$ = 64$$
2

AIEEE 2004

MCQ (Single Correct Answer)
One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with one mole of diatomic gas $$\left( {\gamma = 7/5} \right)$$. What is $$\gamma $$ for the mixture? $$\gamma $$ Denotes the ratio of specific heat at constant pressure, to that at constant volume
A
$$35/23$$
B
$$23/15$$
C
$$3/2$$
D
$$4/3$$

Explanation

$${{{n_1} + {n_2}} \over {\gamma - 1}} = {{{n_1}} \over {{\gamma _1} - 1}} + {{{n_2}} \over {{\gamma _2} - 1}}$$
$$ \Rightarrow {{1 + 1} \over {\gamma - 1}}$$
$$ = {1 \over {{5 \over 3} - 1}} + {1 \over {{7 \over 5} - 1}}$$
$$ \Rightarrow \gamma = {3 \over 2}$$
3

AIEEE 2003

MCQ (Single Correct Answer)
The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by
A
Rayleigh Jeans law
B
Planck's law of radiation
C
Stefan's law of radiation
D
Wien's law

Explanation

Wein's law correctly explanations the spectrum
4

AIEEE 2003

MCQ (Single Correct Answer)
According to Newton's law of cooling, the rate of cooling of a body is proportional to $${\left( {\Delta \theta } \right)^n},$$ where $${\Delta \theta }$$ is the difference of the temperature of the body and the surrounding, and $$n$$ is equal to
A
two
B
three
C
four
D
one

Explanation

$$ - {{dQ} \over {dt}} \propto \left( {\Delta \theta } \right)$$

Questions Asked from Heat and Thermodynamics

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