Tag: measurement and effects of heat

Quizzes (6) Questions (86)

Questions Related to measurement and effects of heat

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

At constant pressure how much fraction of heat supplied to gas is converted into mechanical work ?  

  1. $\dfrac { \gamma -1 }{ \gamma } $

  2. $\dfrac { \gamma }{ \gamma -1 } $

  3. $\gamma -1$

  4. $\dfrac { \gamma }{ \gamma +1 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

At constant pressure, dQ = nCp dT and dW = P dV = nR dT. The fraction of heat converted to work is dW/dQ = (nR dT) / (nCp dT) = R/Cp. Since Cp = gamma*R / (gamma-1), the fraction is R / (gamma*R / (gamma-1)) = (gamma-1)/gamma.

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

A gas compressed to half of its volume at ${30}^{o}C$. Upto what temperature should it be heated, so that its volume increase to double of its original volume?

  1. ${60}^{o}C$

  2. $303K$

  3. $606K$

  4. $1212K$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using P1V1/T1 = P2V2/T2. Since pressure is constant, V1/T1 = V2/T2. V1 = V, V2 = 2V. T1 = 30 + 273 = 303K. V/303 = 2V/T2. T2 = 606K.

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

A gas follows $VT^2 =$ const. Its volume expansion coefficient will be :-

  1. $\dfrac{2}{T}$

  2. $-\dfrac{2}{T}$

  3. $\dfrac{3}{T}$

  4. $-\dfrac{3}{T}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} \gamma =\dfrac { 1 }{ V } \left( { \dfrac { { dV } }{ { dT } }  } \right)  \ P{ T^{ 2 } }=cons\tan  t \ \dfrac { { nRT } }{ V } { T^{ 2 } }=cons\tan  t \ \therefore \gamma =\dfrac { 3 }{ T }  \ Hence,\, C\, the\, \, correct\, option\, .\,  \end{array}$

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

A one litre flask contain some mercury. It is found that at different temperatures the volume of air inside the flask remain same. the volume of mercury taken in the flask is (coefficient of linear expansion of volume expansion of $Hg$ is $1.8\times { 10 }^{ -4 }/ _{  }^{ o }{ C }$ 

  1. $150ml$

  2. $750ml$

  3. $1000ml$

  4. $700ml$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the volume of air to remain constant, the expansion of the mercury must equal the expansion of the flask. V_Hg * gamma_Hg * dT = V_flask * gamma_flask * dT. Assuming gamma_flask is negligible or given, we solve for V_Hg. If gamma_flask is 0, V_Hg = V_flask * (gamma_flask/gamma_Hg). The question implies a specific balance.

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

A uniform steel rod has length $\ell$ at $0^oC$. Now one of its end is kept in ice $(0^oC)$ and the other end is kept in steam $(100^oC)$. If the coefficient of thermal expansion of the rod is $\alpha,$how much is the thermal expansion of the rod at steady state? 

  1. $50\ \alpha\ell$

  2. $100\ \alpha\ell$

  3. $200\ \alpha\ell$

  4. $150\ \alpha\ell$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Thermal expansion is defined as the change in length due to a change in temperature. Since the rod is at steady state with one end at 0C and the other at 100C, the temperature varies linearly along the rod, resulting in an average temperature of 50C. The expansion is given by delta L = L * alpha * delta T, where delta T is the difference between the average temperature and the initial temperature (50 - 0 = 50).

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

An inflated rubber balloon contains one mole of an ideal gas. Has a pressure p, volume V and temperature T. if the temperature rises to 1.1 T, and the volume is increase to 1.05 V, the final pressure will be:

  1. 1.04p

  2. 1.2 p

  3. less than p

  4. between p and 1.1.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$PV=nRT\rightarrow (1)\ P _1(1.05V)=nR(1.1T)\rightarrow (2)\ \Rightarrow (1)\div(2)\ \Rightarrow \cfrac{P}{1.05P _1}=\cfrac{1}{1.1}\ \Rightarrow P _1=\cfrac{1.1P}{1.05}=1.047P$

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

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:

  1. 64.6cm of Hg

  2. 60.6cm of Hg

  3. 58.6cm of Hg

  4. 52.6cm of Hg
Reveal answer Fill a bubble to check yourself
A Correct answer
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
Multiple choice physics measurement and effects of heat thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

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

  1. $3\alpha /2$

  2. $2\alpha /3$

  3. $\alpha $

  4. $\alpha /3$
Reveal answer Fill a bubble to check yourself
C Correct answer
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,

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

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:

  1. 120 cm of Hg

  2. 140 cm of Hg

  3. 160 cm of Hg

  4. 180 cm of Hg
Reveal answer Fill a bubble to check yourself
C Correct answer
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, $P _2=\dfrac{P _1V _1}{V _2}=\dfrac{80 \times V _1}{V _1/2}=160\,cm\,of\,Hg$