Tag: temperature and heat

Questions Related to temperature and heat

Cooking utensils are made up of 

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

  1. Good conductors of heat

  2. bad conductors of heat

  3. neither good conduction not bad conductors of heat

  4. None of these

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Correct Option: A

$1\ kcal $ per hour of heat flowing through a rod of iron. When the rod is cut down to $4$ pieces then what will be the heat flowing through each piece having same differential temperature?

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

  1. $1 / 2\ \mathrm { kcal }$

  2. $1 / 4\ \mathrm { kcal }$

  3. $1\ \mathrm { kcal }$

  4. $1 / 15\ \mathrm { kcal }$.

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Correct Option: A

A metal rod of length $2m$ has cross sectional area $2A$ and as shown in figure$.$ The ends are maintained at temperature $100^0C$ and $70^0C$.$ The tem[temperature at middle point C is

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

  1. $90^0C$

  2. $30^0C$

  3. $45^0C$

  4. $60^0C$

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Correct Option: A
Explanation:

$\begin{array}{l} Let\, \, q\, \, be\, \, temperatrure\, \, middle\, \, po{ { int } }\, \, C\, and\, \, in\, \, series\, \, rate\, \, of\, \, heat\, \, flow\, \, is\, \, same \ K\left( { 2A } \right) \left( { 100-\theta  } \right) =KA\left( { \theta -70 } \right)  \ 200-2\theta =\theta -70 \ 3\theta =270 \ \theta ={ 90^{ 0 } }C \end{array}$

Hence,
option $(A)$ is correct answer.

The thermal conductivity of a rod depends on :

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

  1. length

  2. mass

  3. area of cross-section

  4. material of rod

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Correct Option: D
Explanation:

Thermal conductivity is a material property.
It does not depend on area of cross section, length and mass of the rod.
option (D) is the correct answer.

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