Tag: measurement and effects of heat

Questions Related to measurement and effects of heat

A given amount of gas occupies 1000cc at 27$^{0}$ C and 1200cc and 87$^{0}$ c. What is its volume  coefficient of expansion

physics measurement and effects of heat thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $\frac{1}{273}^{0}C^{-1}$

  2. $\frac{1}{173}^{0}C^{-1}$

  3. $173^{0}C^{-1}$

  4. $273^{0}C^{-1}$

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Correct Option: A
Explanation:

We know , $\alpha =\frac { { V } _{ 2 }-{ V } _{ 1 } }{ { V } _{ 1 }{ t } _{ 2 }-{ V } _{ 2 }{ t } _{ 1 } } $
Substituting the values ${ V } _{ 2 }=1200cc$ , ${ V } _{ 1 }=1000cc$, ${ t } _{ 2 }={ 87 }^{ \circ  }C$, ${ t } _{1}={ 27 }^{ \circ  }C$.
$\therefore \alpha =\frac { 200 }{ \left( 87000-32400 \right)  } $
$\therefore \alpha ={ \frac { 1 }{ 273 }  }^{ \circ  }{ C }^{ -1 }$

The coefficient of volume expansion of liquid is $\gamma$. The fractional change in its density for $\triangle T$ rise in temperature is ?

physics measurement and effects of heat thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $\gamma \triangle T$

  2. $\dfrac{\triangle T}{\gamma}$

  3. $1+\gamma \triangle T$

  4. $1-\gamma \triangle T$

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Correct Option: A
Explanation:

On thermal expansion,

Volumetric expansion is given by
$V=V _0(1+\gamma \Delta T)$. . . . . . . .(1)
We know that, density, $d=\dfrac{mass}{volume}$
$d=\dfrac{m}{V}$
where, $m=$ constant
$d\propto \dfrac{1}{V}$
Density of the liquid varies as

$d=d _0(1+\gamma \Delta T)$
$d=d _0+d _0\gamma \Delta T$
Fractional change in density is 
$\dfrac{d-d _0}{d _0}=\gamma \Delta T$
$\dfrac{\Delta d}{d _0}=\gamma \Delta T$
The correct option is A.

$1$ mole of a gas with $\gamma =\dfrac{7}{5}$ is mixed with $1$ mole of gas with $\gamma =\dfrac{5}{3}$, the value of $\gamma$ of the resulting mixture of.

physics measurement and effects of heat thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $\dfrac{7}{5}$

  2. $\dfrac{2}{5}$

  3. $\dfrac{3}{2}$

  4. $\dfrac{12}{7}$

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Correct Option: C
Explanation:

${ Y } _{ mis }=\cfrac { { n } _{ 1 }C{ \rho  } _{ 1 }+{ n } _{ 2 }C{ \rho  } _{ 2 } }{ { n } _{ 1 }C{ \gamma  } _{ 1 }+{ n } _{ 2 }C{ \gamma  } _{ 2 } } $

${ C\rho  } _{ 1 }=\cfrac { 5 }{ 2 } R$ then its $C{ v } _{ 1 }=\cfrac { 3 }{ 2 } R$
Because ${ C } _{ \rho  }-{ C } _{ v }=R$
for diatomic gas ${ C\rho  } _{ 2 }=\cfrac { 7R }{ 2 } $ then ${ Cv } _{ 2 }=\cfrac { 5 }{ 2 } R$
${ Y } _{ mis }=\cfrac { { n } _{ 1 }\times \cfrac { 5 }{ 2 } R+{ n } _{ 2 }\times \cfrac { 7 }{ 2 } R }{ { n } _{ 1 }\times \cfrac { 3 }{ 2 } R+{ n } _{ 2 }\times \cfrac { 5 }{ 2 } R } $
Here ${ n } _{ 1 }={ n } _{ 2 }=1$
${ Y } _{ mis }=\cfrac { 3 }{ 2 } $

If $T$ represent the absolute temperature of an ideal gas, the volume coefficient of thermal expansion at constant pressure, is :

physics measurement and effects of heat thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $T$

  2. $T^2$

  3. $1/T$

  4. $1/T^2$

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Correct Option: C
Explanation:

From the definition of $\gamma _p$ 


We have $V _t=V _0(1+\gamma _pt)$..........(1) 

Again from Charle's law, $V _t=V _0(1+\dfrac{1}{T}t)$...........(2)  

Comparing (1) and (2), 

$\gamma _p=\dfrac{1}{T}$

Hence,option C is correct.

A man wishes to fit an aluminium ring on steel rod of 1 cm diameter and found it is 0.01 cm smaller in diameter. How much should the on temperature be raised before it just slips on the
$(\alpha _A = 25 \times 10^{-6}/^oC;$ $10 \times 10^{-6}/^oC)$

physics measurement and effects of heat sources of heat introduction to heat measuring temperature

  1. $40^oC$

  2. $50^oC$

  3. $25^oC$

  4. $60^oC$

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Correct Option: A
Explanation:

${l _2} = {l _1}\left( {1 + {\alpha _A}\Delta T} \right)$

${l _2} = {l _1} + {l _1}{\alpha _A}\Delta T$

$\displaystyle {{{l _2} - {l _1}} \over {{l _1}}} = {\alpha _A}\Delta T$

$\displaystyle {{0.01 \times {{10}^{ - 2}}} \over {1 \times {{10}^{ - 2}} \times 25 \times {{10}^{ - 6}}}} = \Delta T$

$\Delta T = {40^0}C$

Which of the following physical quantities is measured in calories ? 

physics measurement and effects of heat sources of heat introduction to heat measuring temperature

  1. Heat energy

  2. Force

  3. Momentum

  4. Temperature

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Correct Option: A
Explanation:

1 calorie: The amount of energy required to warm $1\ g$ of air-free water from $14.5^oC\ to\ 15.5^oC$ at a constant pressure of $101.325\ kPa$ $(1 atm)$

Name the S.I. unit of heat.

physics measurement and effects of heat sources of heat introduction to heat measuring temperature

  1. Joule

  2. Kelvin

  3. Degree centigrade

  4. All of the above

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Correct Option: A
Explanation:

Answer is (A).

It has the same unit as of energy that's Joule.

State the S.I. unit of heat capacity.

physics measurement and effects of heat sources of heat introduction to heat measuring temperature

  1. $ J^{-1}K^{-1}$

  2. $ JK^{-2}$

  3. $ JK$

  4. $ JK^{-1}$

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Correct Option: D
Explanation:

The S.T. unit of heat capacity is heat required per degree rise in temperature. So it is $JK^{-1}$

1 cal = _________

physics measurement and effects of heat sources of heat introduction to heat measuring temperature

  1. 10 joules

  2. 4.18 joules

  3. 4.18 dynes

  4. None of these

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Correct Option: B
Explanation:

1 cal = 4.18 joules

C.G.S unit of heat is calorie.
S.I. unit of heat is joule.

The SI unit of heat is:

physics measurement and effects of heat sources of heat introduction to heat measuring temperature

  1. calorie

  2. joule

  3. dyne

  4. newton

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Correct Option: B