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 principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

If for hydrogen $C _p-C _v=m$ and for nitrogen $C _p-C _v=n$, where $C _p$ and $C _v$ refer to specific heats per unit mass respectively at constant pressure and constant volume, the relation between $m$ and $n$ is (molecular weight of hydrogen$=2$ and molecular weight of nitrogen$=14$)

  1. $n=14m$
  2. $n=7m$
  3. $m=7n$
  4. $m=14n$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For hydrogen, $C _P-C _V=\dfrac{1}{M _{H _2}}\dfrac{dQ}{dT}=m$

For nitrogen, $C _P-C _V=\dfrac{1}{M _{N _2}}\dfrac{dQ}{dT}=n$
$\implies \dfrac{m}{n}=\dfrac{M _{N _2}}{M _{H _2}}=\dfrac{14}{2}=7$

Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

The average degree of freedom per molecule for a gas are $6$. The gas performs $25 J$ of work when it expands at a constant pressure. The heat absorbed by gas is 

  1. $75 \ J$
  2. $100 \ J$
  3. $150\ J$
  4. $125 \ J$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a gas with 'n' degrees of freedom:
$\gamma = 1 + \dfrac{2}{n} = 1 + \dfrac{2}{6} = \dfrac{4}{3}$
$C _{p} = \dfrac{\gamma R}{\gamma - 1} = 4R$
$C _{v} = \dfrac{R}{\gamma - 1} = 3R$

Heat supplied for constant pressure process is $nC _{p}\Delta T$

Change in internal energy $nC _{v} \Delta T$
$\dfrac{\Delta U}{Q} = \dfrac{C _{v}}{C _{p}} = \dfrac{1}{\gamma} = \dfrac{3}{4}$

Hence $\dfrac{W}{Q} = 1 - \dfrac{\Delta U}{Q} = \dfrac{1}{4}$
$\dfrac{W}{Q}=1-\dfrac{3}{4}=\dfrac{1}{4}$
$\implies Q = 100J$

Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

What is the ratio of specific heats of constant pressure and constant volume for $NH _3$

  1. 1.33

  2. 1.44

  3. 1.28

  4. 1.67
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ammonia (NH3) is a polyatomic gas. The ratio of specific heats (gamma) for polyatomic gases is typically lower than that of diatomic gases (1.4), and 1.28 is the standard value for NH3.

Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

A reversible adiabatic path on a P- V diagram foran ideal gas passes through state A where P = 0.7$\times $ ${ 10 }^{ 2  }$ N/${ m }^{ -2 }$ and v=0.0049 $ { m }^{ 3  }$, The ratio of specific heat of the gas is 1.4 , The slop of patch at A is:

  1. $2.0 \times{ 10 }^{ 3\quad }{ Nm }^{ -5 }$
  2. $1.0 \times{ 10 }^{ 3\quad }{ Nm }^{ -8}$
  3. $-2.0\times{ 10 }^{ 7\quad }{ Nm }^{ -3 }$
  4. $-1.0\times{ 10 }^{ 3\quad }{ Nm }^{ -5 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

The value of the ratio ${C} _{p}/{C} _{v}$ for hydrogen is $1.67$ a $30K$ but decreases to $1.4$ at $300K$ as more degrees of freedom become active. During this rise in temperature (assume H2 as ideal gas),

  1. ${C} _{p}$ remains constant but ${C} _{v}$ increases
  2. ${C} _{p}$ decreases but ${C} _{v}$ increases
  3. Both ${C} _{p}$ and ${C} _{v}$ decreases by the same amount
  4. Both ${C} _{p}$ and ${C} _{v}$ increase by the same amount
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

A polyatomic gas with six degrees of freedom does $25\ J$ of work when it is expanded at constant pressure. The heat given to the gas is

  1. $100\ J$
  2. $150\ J$
  3. $200\ J$
  4. $250\ J$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Degree of freedom, $f=6$
$\Rightarrow C _v=\dfrac{fR}{2}=3R$
$\Rightarrow C _p=C _v+R=4R$
Also work done $=\Delta W$=25J


Thus for isobaric process applying first law,
Heat given($\Delta Q$) $=$ internal energy change$(\Delta U)+\Delta W$
$\Rightarrow nC _p\Delta T=nC _v\Delta T+\Delta W$
$\Rightarrow 4nR\Delta T=3nR\Delta T +25J$
$\Rightarrow nR\Delta T=25J$
Hence, $ \Delta Q=4\times 25=100J$

Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

A gas expands against a constant external pressure of  $2.00 atm, $ increasing its volume by $ 3.40 L.$   Simultaneously, the system absorbs  $400 J $ of heat from its surroundings. What is  $ \Delta E ,$  in joules, for this gas?

  1. $- 689$
  2. $-289$
  3. $+400$
  4. $+289$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the first law of thermodynamics, delta E = Q - W. Work done by the gas is P * delta V = 2.00 atm * 3.40 L = 6.80 L*atm. Converting to Joules (1 L*atm = 101.3 J), W = 6.80 * 101.3 = 688.84 J. Thus, delta E = 400 J - 688.84 J = -288.84 J, which rounds to -289 J.

Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

$C _{P}$ and $C _{V}$ are specific heats at constant pressure and constant volume, respectively. It is observed that $C _{P} - C _{V} = a$ for hydrogen gas $C _{P} - C _{V} = b$ for nitrogen gas. The correct relation between $a$ and $b$ is

  1. $a = b$
  2. $a = 14b$
  3. $a = 28b$
  4. $a = \dfrac {1}{14}b$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For any ideal gas, Cp - Cv = R (in molar terms). If 'a' and 'b' refer to specific heats (per unit mass), then Cp - Cv = R/M, where M is molar mass. For hydrogen, M=2; for nitrogen, M=28. Thus, a = R/2 and b = R/28. Therefore, a/b = 28/2 = 14, so a = 14b.

Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

If $C _{p} and C _{v}$ denoto the specific heats of nitron per unit mass at constant pressure and constant volume rest then 

  1. $C _{p} and C _{v}$=R/28
  2. $C _{p} and C _{v}$=R/14
  3. $C _{p} and C _{v}$=R
  4. $C _{p} and C _{v}$=28R
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Mayer's relation $C _{p}-C _{v}= R/m$

$C _{p}-C _{v}=\dfrac{R}{m}$
for nitrogen $m=28$
$ \therefore C _{p}- C _{v^{2}} R/28$

Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

Ration of $C _p$ and $C _v$ depends upon temperatures according to the following relation

  1. $\gamma \propto T$
  2. $\displaystyle \gamma \propto \frac{1}{T}$
  3. $\gamma \propto \sqrt{T}$
  4. $\gamma \propto T^o$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\gamma =\dfrac{C _p}{C _v}$ i.e, ratio of specific heat capacity at constant pressure and specific heat capacity at constant volume. It doesn't depend on temperature, i.e, it is independent of temperature.

Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

Which type of ideal gas will have the largest value for $C _p-C _v?$

  1. Monoatomic

  2. Diatomic

  3. Polyatomic

  4. The value will be the same for all
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For all ideal gases, the difference between molar heat capacity at constant pressure and constant volume is defined by the universal gas constant, Cp - Cv = R. This value is independent of the atomicity of the gas.

Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

For an ideal gas

  1. $C _p$ is less than $C _v$
  2. $C _p$ is equal to $C _v$
  3. $C _p$ is greater than $C _v$
  4. $C _p=C _v=0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 For an ideal gas, $C _p$ is greater than $C _v$ because when gas is heated at constant volume, whole of the heat supplied is used to increase the temperature only but when gas is heated at constant pressure, the heat supplied is used to increases both temperature and the volume of gas (heat is used to do work)

The correct option is C.