Tag: thermal expansion of fluids

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Questions Related to thermal expansion of fluids

Multiple choice physics measurement and effects of heat thermal expansion in gases thermal expansion of fluids 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

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

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

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

  4. $273^{0}C^{-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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)  } $
$\therefore \alpha ={ \frac { 1 }{ 273 }  }^{ \circ  }{ C }^{ -1 }$

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

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

  1. $\gamma \triangle T$

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

  3. $1+\gamma \triangle T$

  4. $1-\gamma \triangle T$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

$1$ 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.

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

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

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

  4. $\dfrac{12}{7}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 } $

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

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

  1. $T$

  2. $T^2$

  3. $1/T$

  4. $1/T^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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).

  1. $25$ cm of HG

  2. $35$ cm of HG

  3. $55$ cm of HG

  4. $85$ cm of HG
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the ideal gas law PV = nRT, since the amount of gas and the total volume are constant, we relate the pressures and temperatures. The pressure of the gas at 0C (273K) and 127C (400K) must satisfy the condition that the total length of the air columns remains constant (90cm total). Solving the system of equations for the pressure P leads to 35 cm of Hg.

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

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

  1. $2 m^3$

  2. $4 m^3$

  3. $6 m^3$

  4. $8 m^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The efficiency of a Carnot-like cycle involving adiabatic and isothermal steps is 1 - (T_cold / T_hot). For an ideal gas, the temperature ratio is related to volume ratios via adiabatic relations (T * V^(gamma-1) = constant). Given efficiency 3/4, the ratio of temperatures is 1/4, which allows solving for V3 in terms of V1.

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

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 :

  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. ${ \Upsilon } _{ l }\quad =\quad 2{ \alpha } _{ s }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A solid floats if its density is less than the liquid density. If the solid sinks upon cooling, it means the density of the solid increased more than the density of the liquid, or the liquid density decreased relative to the solid. Since volume expansion coefficients are related to density changes, the condition for the solid to sink is that the liquid's volume expansion coefficient is greater than the solid's volume expansion coefficient (3 * alpha).

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

The SI unit for the coefficient of cubical expansion is

  1. $^\circ C$

  2. $per^\circ C$

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

  4. none of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
The SI unit of coefficient of cubical expansion is $K^{-1}$
$\gamma =\cfrac { 1 }{ V } \cfrac { dV }{ dT } =\cfrac { 1 }{ { metre }^{ 3 } } \cfrac { { metre }^{ 3 } }{ K } ={ K }^{ -1 }$
Multiple choice physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

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.

  1. R

  2. $R^3$

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

  4. $R^{2/3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Density rho = M / V = M / ((4/3) * pi * R^3). Taking the logarithmic derivative with respect to time, (1/rho) * (d_rho/dt) = -3 * (1/R) * (dR/dt). Since the fractional change in density is constant, (1/R) * (dR/dt) must be constant. The velocity of the surface is v = dR/dt, so v = constant * R.

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

  1. $1|T$

  2. <span>$2|T$</span>

  3. <span>$3|T$</span>

  4. <span>$4|T$</span>
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For an ideal gas, PV = nRT. Given PT^2 = constant, substitute P = nRT/V into the equation to get (nRT/V) * T^2 = constant, which implies T^3 / V = constant, or V proportional to T^3. The coefficient of volume expansion gamma is (1/V) * (dV/dT). Differentiating V = k * T^3 gives dV/dT = 3 * k * T^2, so gamma = (3 * k * T^2) / (k * T^3) = 3/T.