Tag: physics

Questions Related to physics

The pressures of a gas in the bulb of constant volume gas thermometer at 0$^{0}$ C are 54.6 cm and 74.6cm of Hg respectively. The pressure at 50$^{0}$ C is:

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

  1. 64.6cm of Hg

  2. 60.6cm of Hg

  3. 58.6cm of Hg

  4. 52.6cm of Hg

Show answer
Correct Option: A
Explanation:
For a constant volume thermometer,
$P\propto T$ , the slope is given by
$\beta =\dfrac { { P } _{ 100 }-{ P } _{ 0 } }{ 100-0 }  $
$\beta =\dfrac { 74.6-54.6 }{ 100 }  $
$\beta$=0.2.
Now Applying equation for straight line,
${ P } _{ 50 }=T\beta +{ P } _{ 0 }$ 
${ P } _{ 50 }=50\times 0.2+54.6$
${ P } _{ 50 }=64.6$cm of Hg

A vessel contains 1 mole of an ideal monoatomic gas. The coefficient of volume expansion of the gas is $\alpha $. 2 moles of a diatmoic; ideal gas is then introduced into the same vessel. The coefficient of the volume expansion of the mixture will be

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

  1. $3\alpha /2$

  2. $2\alpha /3$

  3. $\alpha $

  4. $\alpha /3$

Show answer
Correct Option: C
Explanation:

The volume coefficient of gas is given by,
${ \alpha  } _{ V }={ \left( \frac { 1 }{ V } \frac { \partial V }{ \partial T }  \right)  } _{ p }$
From the above equation it can be seen that it is independent of the number of moles,

If at $60^\circ$C and 80 cm of mercury pressure, a definite mass of a gas is compressed slowly, then the final pressure of the gas if the final volume is half of the initial volume $ (\gamma = \dfrac { 3 }{ 2 }$) is:

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

  1. 120 cm of Hg

  2. 140 cm of Hg

  3. 160 cm of Hg

  4. 180 cm of Hg

Show answer
Correct Option: C
Explanation:
Given initial pressure, $P _1=80\,cm\,of\,Hg$

If the gas is compressed slowly, then the process is isothermal.

At constant temperature,

$P _1V _1=P _2V _2$

Given, 

Final volume is half of the initial volume.

That is, $V _2=\dfrac{V _1}{2}$

Final pressure, $P _2=\dfrac{P _1V _1}{V _2}=\dfrac{80 \times V _1}{V _1/2}=160\,cm\,of\,Hg$

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

Show answer
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. $1-\gamma \triangle T$

Show answer
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. $\dfrac{12}{7}$

Show answer
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. $1/T^2$

Show answer
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

Show answer
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. $8 m^3$

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

Show answer
Correct Option: B