Tag: volume elasticity constant of gases

Questions Related to volume elasticity constant of gases

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 glass capillary tube sealed at both ends is 100cm long. It lies horizontally with the middle 10cm containing mercury. The two ends of the tube which are equal in length contain air at $27 ^ { 0 } \mathrm { C }$ at a pressure of 76cm of Hg. Now the air column at one end of the tube is kept at $0 ^ { 0 } \mathrm { C }$ and the other end is maintained at $127 ^ { \circ } C$. Calculate the pressure of the air column at $0 ^ { \circ } \mathrm { C }$. (Neglect the change in volume of Hg and glass).

physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $25$ cm of HG

  2. $35$ cm of HG

  3. $55$ cm of HG

  4. $85$ cm of HG

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Correct Option: B

One mole of n ideal monatomic  gas undergoes the following four reversible processes:
Step I: It is first compresses adiabatically from volume $V _1$ to $1m^3$.
Step II: then expanded isothermally to volume $10 m^3$.
Step III: then expanded adiabatically to volume $V _3$.
Step IV: then compressed isothermally to volume $V _1$.
If the efficiency of the above cycle is $3/4$ then V, is

physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $2 m^3$

  2. $4 m^3$

  3. $6 m^3$

  4. $8 m^3$

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Correct Option: C

Solid floating in a liquid . On decreasing the temperature solid sinks into the liquid . If ${ \Upsilon  } _{ l }\quad and\quad { \alpha  } _{ s }$ are volume expansion coefficient of liquid and linear expansion coefficient of solid , then :

physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. ${ \Upsilon } _{ l }\quad <\quad 3{ \alpha } _{ s }$

  2. ${ \Upsilon } _{ l }\quad >\quad 3{ \alpha } _{ s }$

  3. ${ \Upsilon } _{ l }\quad =\quad 3{ \alpha } _{ s }$

  4. ${ \Upsilon } _{ l }\quad =\quad 2{ \alpha } _{ s }$

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Correct Option: B

The SI unit for the coefficient of cubical expansion is

physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $^\circ C$

  2. $per^\circ C$

  3. $cm^{2}/^\circ C$

  4. none of these

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Correct Option: D
Explanation:
The SI unit of coefficient of cubical expansion is $K^{-1}$
$\gamma =\cfrac { 1 }{ V } \cfrac { dV }{ dT } =\cfrac { 1 }{ { metre }^{ 3 } } \cfrac { { metre }^{ 3 } }{ K } ={ K }^{ -1 }$

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\dfrac{1}{p}\dfrac{d\rho}{dt}\right)$ is constant. The velocity v of any point on the surface of the expanding sphere is proportional to.

physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. R

  2. $R^3$

  3. $\dfrac{1}{R}$

  4. $R^{2/3}$

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Correct Option: A
an ideal gas is expanding such that $PT^2$ $=costant$ The coefficient of volume expansion of the gas is__? 
physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $1|T$

  2. $2|T$

  3. $3|T$

  4. $4|T$

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Correct Option: C