Tag: conduction

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Questions Related to conduction

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Three copper blocks of masses ${ M } _{ 1 },{ M } _{ 2 }$ and ${ M } _{ 3 }$ kg respectively are brought into thermal contact till they reach equilibrium. Before contact. they were at ${ T } _{ 1 },{ T } _{ 2 },{ T } _{ 3 }$ $\left( { T } _{ 1 }>{ T } _{ 2 }>{ T } _{ 3 } \right) .$ Assuming there is no heat loss to the surrounding, the equilibrium temperature T (s is specitc heat of copper)

  1. $T=\dfrac { { T } _{ 1 }+{ T } _{ 2 }+{ T } _{ 3 } }{ 3 } $

  2. $T=\dfrac { { M } _{ 1 }{ T } _{ 1 }+{ M } _{ 2 }{ T } _{ 2 }+{ M } _{ 3 }{ T } _{ 3 } }{ { M } _{ 1 }+{ M } _{ 2 }+{ M } _{ 3 } } $

  3. $T=\dfrac { { M } _{ 1 }{ T } _{ 1 }+{ M } _{ 2 }{ T } _{ 2 }+{ M } _{ 3 }{ T } _{ 3 } }{ 3{ (M } _{ 1 }+{ M } _{ 2 }+{ M } _{ 3 }) } $

  4. $T=\dfrac { { M } _{ 1 }{ T } _{ 1 }s+{ M } _{ 2 }{ T } _{ 2 }s+{ M } _{ 3 }{ T } _{ 3 }s }{ { M } _{ 1 }+{ M } _{ 2 }+{ M } _{ 3 } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Two walls of thickness   $d _ { 1 }$   and   $d _ { 2 }$   thermal conductivities  $K _ { 1 }$  and  $K _ { 2 }$  are in contact. In the steady state if the temperatures at the outer surfaces are  $T _ { 1 }$  and  $T _ { 2 },$  the temperature at the common wall will be

  1. $\dfrac { K _ { 1 } T _ { 1 } + K _ { 2 } T _ { 2 } } { d _ { 1 } + d _ { 2 } }$

  2. $\dfrac { K _{ { 1 } }T _{ 1 }d _{ { 2 } }+K _{ { 2 } }T _{ { 2 } }d _{ { 1 } } }{ K _{ { 1 } }d _{ { 2 } }+K _{ { 2 } }d _{ { 1 } } } $

  3. $\dfrac { \left( K _ { 1 } d _ { 1 } + K _ { 2 } d _ { 2 } \right) T _ { 1 } T _ { 2 } } { T _ { 1 } + T _ { 2 } }$

  4. $\dfrac { K _{ { 1 } }d _{ { 1 } }T _{ 1 }+K _{ { 2 } }d _{ { 2 } }T _{ { 2 } } }{ K _{ { 1 } }d _{ { 1 } }+K _{ { 2 } }d _{ { 2 } } } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l} Under\, steady\, state\, heat\, flux\, per\, unit\, area\, k\left( { \frac { { dT } }{ { dx } }  } \right)  \ is\, same\, across\, two\, walls.\, hence,\, we\, have \ { K _{ 1 } }\dfrac { { { T _{ 1 } }-{ T _{ c } } } }{ { { d _{ 1 } } } } ={ K _{ 2 } }\dfrac { { { T _{ c } }-{ T _{ 2 } } } }{ { { d _{ 2 } } } }  \ where\, { T _{ c } }\, is\, common\, wall\, temperature.\, \, solving\, for\, { T _{ c } }\, we\, will\, get \ { T _{ c } }=\dfrac { { { T _{ 1 } }+\alpha { T _{ 2 } } } }{ { \alpha +1 } }  \ Where\, \alpha =\dfrac { { { d _{ 1 } } } }{ { { d _{ 2 } } } } \, \dfrac { { { k _{ 2 } } } }{ { { k _{ 2 } } } }  \end{array}$

$\begin{array}{l} On\, putting\, the\, value\, of\, \alpha =\dfrac { { { d _{ 1 } } } }{ { { d _{ 2 } } } } .\dfrac { { { k _{ 1 } } } }{ { { k _{ 2 } } } }  \ Then,\, { T _{ c } }=\dfrac { { { k _{ 1 } }{ T _{ 1 } }{ d _{ 2 } }+{ k _{ 2 } }{ T _{ 2 } }{ d _{ 1 } } } }{ { { k _{ 1 } }{ d _{ 2 } }+{ k _{ 2 } }{ d _{ 1 } } } }  \end{array}$
Hence,Option $B$ is the correct answer.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Two rods of length  $\mathrm { d _ { 1 } } ,$  and  $\mathrm { d _ { 2 } } ,$  and coefficient of thermal conductivities  $\mathrm { K } _ { 1 }$  and  $\mathrm { K } _ { 2 }$  are kept touching each other. Both have the same area of cross-section. The equivalent of thermal conductivity is

  1. $K _ { 1 } + K _ { 2 }$

  2. $\mathrm { K } _ { 1 } \mathrm { d } _ { 1 } + \mathrm { K } _ { 2 } \mathrm { d } _ { 2 }$

  3. $\dfrac { \mathrm { d } _ { 1 } \mathrm { K } _ { 2 } + \mathrm { d } _ { 2 } \mathrm { K } _ { 2 } } { \mathrm { d } _ { 1 } + \mathrm { d } _ { 2 } }$

  4. $\dfrac { d _ { 1 } + d _ { 2 } } { \left( d _ { 1 } K _ { 2 } \right) + \left( d _ { 2 } K _ { 2 } \right) }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Three roads identical area of cross-section and made from the same metal from the sides of an isosceles triangle ABC, right angled at B. The points A and B are maintained at temperature  T and $ \sqrt {2} T $ respectively. IN the steady state the temperature that only point C is $ T _c $ Assuming that only conduction takes place $ \frac {T _c}{T} is $

  1. $ \frac { 1 }{ \left( \sqrt { 2 } +1 \right) } $

  2. $ \frac { 1 }{ \left( \sqrt { 2 } -1 \right) } $

  3. $ \frac { 1 }{ 2\left( \sqrt { 2 } +1 \right) } $

  4. $ \frac { 1 }{ \sqrt { 3 } \left( \sqrt { 2 } -1 \right) } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Two rods of equal length and area of cross-sectional are kept parallel and lagged between temperature $ 20^o C and 80^oC $ The ration of the effective thermal conductivity to that of the first rod is
 $ \left[ the\quad ration\left( \frac { K _ 1 }{ K _ 2 }  \right) =\frac { 3 }{ 4 }  \right]  $

  1. 7 : 4

  2. 7 : 6

  3. 4 : 7

  4. 7 : 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Fix a lighted candle on a table. Put a glass chimney over the candle in such a way that air can enter the chimney from below. What happens to the flame? 

  1. Continues burning

  2. Flickers off

  3. Flickers off and give smoke

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a chimney is placed over a candle, the air supply is restricted. The lack of sufficient oxygen leads to incomplete combustion, which produces soot (smoke) and causes the flame to become unstable or flicker.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Two spheres of different materials one with double the radius and one - fourth wall thickness of the other, are filled with $r$ ice. If the time taken for complete melting ice in the large radius one is $25 minutes$ and that for smaller one is $16 minutes$, $r$ the ratio of thermal conductivity of the materials of larger sphere to the smaller sphere is $r$

  1. $4:5$

  2. $5:4$

  3. $25:1$

  4. $1:25$
Reveal answer Fill a bubble to check yourself
D Correct answer