Physics

Thermodynamics and Gas Laws

616 Questions

Thermodynamics and gas laws questions test the understanding of ideal gas behavior, work done during thermodynamic processes, and specific heat ratios. Key areas include isothermal, adiabatic, and isobaric expansions along with real gas deviations. These mathematical physics concepts are standard in engineering and general science competitive exams.

Ideal gas equationIsothermal and adiabatic processesThermodynamic workGas kinetic theoryReal gas behavior

Thermodynamics and Gas Laws Questions

Multiple choice zoology respiratory system of human mechanism of respiration respiratory cycle breathing and exchange of gas

According to Boyle's law, the product of:.pressure and volume is a constant. Hence,

  1. if volume of lungs is increased, then pressure decreases proportionately

  2. if volume of lungs is increased, then pressure also increases proportionately

  3. if volume of lungs is increased, then pressure decreases disproportionately

  4. if volume of lungs is increased, then pressure remains the same.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
According to Boyle's law, the product of pressure and volume is a constant. Hence, if the volume of the lungs is increased, then pressure decreases proportionately.
So, the correct answer is 'if volume of lungs is increased, then pressure decreases proportionately'.
Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

At what temperature volume of an ideal gas at $0^oC$  becomes triple by keeping pressure constant

  1. $546^oC$
  2. $182^oC$
  3. $819^oC$
  4. $646^oC$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using Charles's Law (V1/T1 = V2/T2) at constant pressure, if V2 = 3*V1, then T2 = 3*T1. Given T1 = 0 C = 273 K, T2 = 3 * 273 = 819 K. Converting back to Celsius, 819 - 273 = 546 C.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

A container with insulating wall is divided into two equal parts by a partition fitted with a vaive.One part is filled with an ideal gas at pressure P and temperature T, whereas the other part is one part is  completely evacuated. If the valve is suddenly opened, the pressure and temperature of gas will be: 

  1. $P , \cfrac { T } { 2 }$
  2. $\cfrac { P } { 2 } , T$
  3. $\cfrac { P } { 2 } , \cfrac { T } { 2 }$
  4. $P , T$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a free expansion (Joule expansion) into a vacuum. Since the walls are insulating (adiabatic) and no work is done (expansion against vacuum), the internal energy remains constant, meaning temperature T remains constant. The volume doubles, so by PV = nRT, the pressure must halve to P/2.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

The relation PV=RT can describe the behavior of a real gas at :

  1. high temperature and high pressure

  2. high temperature and low pressure

  3. low temperature and low pressure

  4. low temperature and high pressure
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

PV=RT is ideal gas equation and gases behave ideally only at high temperature and low pressure.
Therefore option(B).

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

A real gas behaves as an ideal gas :

  1. at very low pressure and high temperature

  2. high pressure and low temperature

  3. high temperature and high pressure

  4. low pressure and low temperature
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Real gas obeys vanderwaals equation 
$\left( p+\dfrac { n^{ 2 }a }{ V^{ 2 } }  \right) \left( V-nb \right) =nRT$
at high temperature and low pressure
Van der waal equation becomes approximately PV=nRT
Hence gases behave ideally at high temperature and low pressure.
Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

The equation of state of a real gas can be expressed as $(P + \dfrac{a}{V _2}) (V - b) = cT$, where P is the pressure, V the volume, T the absolute temperature and a, b, c are constants. What are the dimensions of 'a'-

  1. $M^0 L^3 T^{-2}$
  2. $ M L^{-2} T^5$
  3. $M L^5 T{-2}$
  4. $M^0 L^3 T^0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\left( {p + \frac{a}{{{V _2}}}} \right)\left( {v - b} \right) = cT$

$p$ is pressure, $V$ is volume and $T$ is temperature
$\begin{array}{l} p=\frac { F }{ A } =\frac { { ML{ T^{ -2 } } } }{ { { L^{ 2 } } } } =M{ L^{ -1 } }{ T^{ -2 } } \ V={ L^{ 3 } } \end{array}$
We cannot add or subtract quantities of different dimensions.
$\begin{array}{l} \therefore p=\frac { a }{ { { V^{ 2 } } } }  \ \Rightarrow a=\frac { p }{ { { V^{ 2 } } } } =\frac { { M{ L^{ -1 } }{ T^{ -2 } } } }{ { { { \left( { { L^{ 3 } } } \right)  }^{ 2 } } } } =M{ L^{ 5 } }{ T^{ -2 } } \end{array}$
Hence, Option $C$ is correct.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Diatomic gas at pressure `P' and volume `V' is compressed adiabatically to 1/32 times the original volume. Then
the final pressure is

  1. P/32

  2. 32 P

  3. 128 P

  4. P/128
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For adiabatic processes, P * V^gamma = constant. For a diatomic gas, gamma = 1.4 or 7/5. P2 = P1 * (V1/V2)^gamma. Here V1/V2 = 32. P2 = P * (32)^(7/5) = P * (2^5)^(7/5) = P * 2^7 = 128P.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

For a real gas, deviations from ideal gas behavior are maximum at 

  1. $-10^o C$ and $5.0 \,atm$
  2. $-10^o C$ and $2.0 \,atm$
  3. $0^o C$ and $1.0 \,atm$
  4. $100^o C$ and $2.0 \,atm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Real gases deviate most from ideal behavior at high pressures and low temperatures, where intermolecular forces and molecular volume become significant.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

As per Langmuir model of adsorption of a gas on a solid surface.

  1. The mass of gas striking a surface area is independent of the pressure of the gas

  2. The adsorption can be multilayer.

  3. The rate of desorption does not depend on the pressure.

  4. The rate of desorption does not depend on the surface are adsorbed.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In Langmuir's model of adsorption of a gas on solids surfaces. The adsorption at a single site on the surface may invoice multiple molecules at the ame time. The mass of gas striking at a given area of surface is independent of the pressure of the gas.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Under which of the following conditions is the law $pV=RT$ obeyed most closely by a real gas?

  1. High pressure and high temperature.

  2. Low pressure and low temperature.

  3. High pressure and low temperature.

  4. Low pressure and high temperature.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At low pressure and high temperature real gas obey PV=RT  i.e. they behave as ideal gas because at high temperature we can assume that there is no force of attraction or repulsion works among the molecules and the volume occupied by the molecules is negligible in comparison to the volume occupied by the gas

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

The behaviour of the gases, which can be easily liquified, is like that of the

  1. triatomic gases

  2. ideal gases

  3. van der Waals gases

  4. all of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Van der Walls equation takes into account inter atomic forces between gas particles which is not considered in the ideal gas model. Since simplicity of  liquification of a gas depends upon forces between its particles, Van der Walls equation is followed by easily liquifieable gases. 


$(P+a(\dfrac { { n }^{ 2 } }{ { V }^{ 2 } } ))(V-nb)=nRT$

Parameter a takes into account interatomic forces.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Read the given statements and choose which is/are on the basis of kinetic theory of gases.

  1. Energy of one molecule at absolute temperature is zero.
  2. $rms$ speeds of different gases are same at same temperature

  3. For one gram of all ideal gases, kinetic energy is same at same temperature.

  4. For one mole of all ideal gases, mean kinetic energy is same at same temperature.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Work done by a system under isothermal change from a volume $V _1$ to $V _2$ for a gas, which obeys vander Waals equation $(V - \beta n) \displaystyle \left ( P + \dfrac{an^2}{V} \right ) = n RT$ is

  1. $\displaystyle n RT log _e \left ( \dfrac{V _2 - n \beta}{V _1 - n \beta} \right ) + an^2 \left ( \dfrac{V _1 - V _2}{V _1 V _2} \right )$
  2. $\displaystyle n RT log _{10} \left ( \dfrac{V _2 - \alpha \beta}{V _1 - \alpha \beta} \right ) + \alpha n^2 \left ( \dfrac{V _1 - V _2}{V _1 V _2} \right )$
  3. $\displaystyle n RT log _e \left ( \dfrac{V _2 - n \alpha}{V _1 - n \alpha} \right ) + \beta n^2 \left ( \dfrac{V _1 - V _2}{V _1 V _2} \right )$
  4. $\displaystyle n RT log _e \left ( \dfrac{V _2 - n \beta}{V _1 - n \beta} \right ) + \alpha^2 \left ( \dfrac{V _1 V _2}{V _1- V _2} \right )$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given Vander Waals equation $(V - \beta n)$ ($P$ $+$ $\dfrac {a{n}^{2}} {{V}^{2}}$) $=$ $nRT$
Work done by the system($W$) = $-$ $\int _{{V} _{1}}^{{V} _{2}} {PdV}$
                                           $=$ $\int _{{V} _{2}}^{{V} _{1}} {PdV}$
From the Vander Waals equation:
$P$ $=$ $\dfrac {nRT} {(V - \beta n)}$ $-$ $\dfrac {a{n}^2} {{V}^{2}}$
Substituting $'P'$ in the Work done, we get
$W$ $=$ $\int _{{V} _{2}}^{{V} _{1}}$ ($\dfrac {nRT} {(V - \beta n)}$ $-$ $\dfrac {a{n}^2} {{V}^{2}}$) $dV$
By integrating we get,
$W$ $=$ $[$ $nRT$ $\log _{e}{(V - \beta n)}$ $-$ ($(-)\dfrac {a{n}^{2}} {V}$) ] $ _{{V} _{2} \rightarrow {V} _{1}}$
$W$ $=$ $nRT$ $\log _{e}{}$ $($$\dfrac { {V} _{2} - \beta n} {{V} _{1} - \beta n} $ $)$ $+$ $a{n}^{2}$$($ $\dfrac {{V} _{1} - {V} _{2}} { {V} _{1}{V} _{2}}$ $)$
Hence, the Correct Option is $'A'$.