Tag: conduction

Questions Related to conduction

The heat capacity of a metal is 4200 J/k. Its water equivalent is-

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

  1. $0.5 kg$

  2. $1 kg$

  3. $1.5 k$

  4. $2 kg$

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Correct Option: A

A steel drill is making 180 revolutions per minute under a constant couple of 5 Nm. If it drills a hole in 7 seconds in a steel block of mass 600 gm, the rise in temperature of the block is: (S=0.I cal/gm/K)

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

  1. $46 ^ { 0 } C$

  2. $1.3 ^ { 0 } C$

  3. $5.2 ^ { 0 } C$

  4. $3 ^ { 0 } C$

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Correct Option: C

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)

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

  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 } } $

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Correct Option: C

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

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

  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 } } } $

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Correct Option: B
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.

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

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

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

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Correct Option: D

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 $

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

  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) } $

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Correct Option: A

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]  $

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

  1. 7 : 4

  2. 7 : 6

  3. 4 : 7

  4. 7 : 8

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Correct Option: A

In engines water is used as coolant, because

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

  1. It good conductor of heat energy.

  2. It has low density.

  3. It has LOW specific heat.

  4. It's bad conductor of heat energy.

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Correct Option: D

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? 

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

  1. Continues burning

  2. Flickers off

  3. Flickers off and give smoke

  4. None of these

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Correct Option: C

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 $r$

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

  1. $4:5$

  2. $5:4$

  3. $25:1$

  4. $1:25$

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Correct Option: D