Physics

Thermodynamics and Gas Laws

626 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

When a heat of Q is supplied to one mole of a monatomic gas $\left ( \gamma =5/3 \right )$, the molar heat capacity of the gas at constant volume is

  1. $ \dfrac{3R}{4}$
  2. $ \dfrac{5R}{4}$
  3. $ \dfrac{7R}{4}$
  4. $\dfrac{3R}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given $\gamma =5/3$

i.e $\displaystyle \dfrac {C _p}{C _v}=\dfrac {5}{3}$
and $C _p-C _v=R$

$\therefore \displaystyle \dfrac {C _v+R}{C _v}=\dfrac {5}{3}$
$\displaystyle 1+\dfrac {R}{C _v}=\dfrac {5}{3}$

$C _v= \dfrac{3R}{2}$
Option D.

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

The molar specific heat of helium at constant volume is $3\ cal/mol^{o}C$ . Heat energy required to raise the temperature of 1gm helium gas by $1^{o}C$ at constant pressure is :

  1. 1.2 cal

  2. 1.25 cal

  3. 3 cal

  4. 4 cal
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Heat added for a constant pressure process is,


$dQ=dU+dW$

$nC _p\Delta T=nC _v\Delta T+nR\Delta T$

Given 1 gm of Helium, number of moles$= 1/4 =0.25$

$R=2\ cal/mol-K$

$dQ=0.25[3(1)+2(1)]=0.25(5)=1.25\ cal$

Option B.

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

When 5 moles of gas is heated from $100^{o}C$ to $120^{o}C$ at constant volume, the change in internal energy is 200 J. The specific heat capacity of the gas is

  1. $5\space Jmol^{-1}K^{-1}$
  2. $4\space Jmol^{-1}K^{-1}$
  3. $2\space Jmol^{-1}K^{-1}$
  4. $1\space Jmol^{-1}K^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Change in internal energy is given by
$dU=nC _v\Delta T$
$200=5(C _v)20$
$C _v=2J/mol.K$
Option C.

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

$n _{1}$ and $n _{2}$ moles of two ideal gases of the thermodynamics constant $\gamma _{1}$ and $\gamma _{2}$ respectively are mixed. $C _{p}/ C _{v}$ for the mixture is

  1. $\dfrac {\gamma _{1} + \gamma _{2}}{2}$
  2. $\dfrac {n _{1}\gamma _{1} + n _{2}\gamma _{2}}{n _{1} + n _{2}}$
  3. $\dfrac {n _{1}\gamma _{2} + n _{2}\gamma _{1}}{n _{1} + n _{2}}$
  4. $\dfrac {n _{1}\gamma _{1}(\gamma _{2} + 1) + n _{2}\gamma _{2}(\gamma _{1} - 1)}{n _{1}(\gamma _{1} - 1) + n _{2}(\gamma _{1} - 1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

1g of $H _{2}$ gas is heated by $1^{o}C$ at constant pressure. The amount of heat spent in expansion of gas is

  1. $\dfrac{4.155}{4.18}cal$
  2. $\dfrac{4.7}{2.1}cal$
  3. $\dfrac{6.8}{2.2}cal$
  4. $\dfrac{1.26}{1.7}cal$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The amount of heat spent in the process will be,
Q = $ nR \Delta T $
Q = $ \dfrac{1}{2} \times 8.314 \times 1 $ J
The same value in calorie will be, Q = $ \dfrac{4.155}{4.185} $ cal

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

The volume of $1\ kg$ of hydrogen gas at $N.T.P$ is $11.2\ m^{3}$. Specific heat of hydrogen at constant volume is $10046J\ kg^{-1}K^{-1}$. Find the specific heat at constant pressure.

  1. $13.8\ kJ/kg-K$
  2. $14.2\ kJ/kg-K$
  3. $16.4\ kJ/kg-K$
  4. $18.3\ kJ/kg-K$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given that,

Mass of hydrogen $m=1\,kg$

Volume of hydrogen $V=11.2\,{{m}^{3}}$

Specific heat of hydrogen at constant volume ${{C} _{V}}=10046\,JK{{g}^{-1}}{{k}^{-1}}$

 We know that,

N.T.P condition as follows

  $ P=1.01\times {{10}^{5}}\,N/{{m}^{2}} $

 $ T={{25}^{0}}C=298\,K $

 Applying gas equation

 $PV=nRT$

 Putting the values in the above equation

 $ PV=nRT $

$ 1.01\times {{10}^{5}}\times 11.2=1\times R\times 298 $

$ R=3795.97\,J/kgk $

 Now according to the Mayer's law

 ${{C} _{P}}-{{C} _{V}}=R$

 Putting the values in the above equation

 $ {{C} _{P}}-{{C} _{V}}=R $

 $ {{C} _{P}}=3795.97+10046 $

$ {{C} _{P}}=13841.97\,JK{{g}^{-1}}{{k}^{-1}} $

Hence, the specific heat of hydrogen at constant pressure is $13841.97\ J/Kg-k$

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

Molar heat capacity of an ideal gas whose molar heat capacity at constant is $C _v$ for process $P=2e^{2v}$( where P is pressure of gas and V is volume of gas)

  1. $C _v + \dfrac{R}{1+2V}$
  2. $C _v + \dfrac{R}{2V}$
  3. $C _v + \dfrac{R}{V}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} By\, u\sin  g\, \, first\, law\, of\, Ther{ { moodynamics } }:- \ dQ=dw+dU \ and,\, also\,  \ dQ=nCdT \ dw=Pdv \ dU=n{ C _{ v } }dT \ Now,\, substituting\, them\, in\, the\, first\, law\, we\, get \ \Rightarrow nCdT=PdV+n{ C _{ n } }dT \ C=\frac { { PdV } }{ { ndT } } +{ C _{ v } } \ To\, find\, \, \frac { { PdV } }{ { ndT } } \, we\, will\, use\, the\, ideal\, gas\, equation \ PV=nRT \ 2V{ e^{ 2V } }=nRT\, \, \, \, \, \, \left[ { \, { { Re } }place\, \, P=2{ e^{ 2v } } } \right]  \ Differentiating\, both\, sides\, with\, respect\, to\, T \ 2\left( { { e^{ 2V } }+2V{ e^{ 2V } } } \right) \frac { { dV } }{ { dT } } =nR \ Now,\, from\, this\, we\, have \ \frac { { PdV } }{ { ndT } } =\frac { R }{ { 1+2v } }  \ So,\, we\, get \ C={ C _{ v } }+\frac { R }{ { 1+2v } }  \ Hence,\, the\, option\, A\, is\, the\, correct\, answer. \end{array}$

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

For a certain gas the heat capacity at constant pressure is greater than that at constant volume by $29.1 J/K$. How many moles of the gas are there?

  1. $13.5 \ mol $
  2. $9.5 \ mol $
  3. $7.5 \ mol $
  4. $3.5 \ mol $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know that for one mole of gas,


${ C } _{ P }-{ C } _{ V }=8.32J/K$

Hence, for n moles,

$n({ C } _{ P }-{ C } _{ V })=8.32n=29.1$

$n=3.5 mol$

Answer is $3.5 mol$

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

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 ${ JK }^{ -1 }{ mol }^{ -1 }$. If the speed of sound in this gas at NTP is 952${ ms }^{ -1 }$, then the heat capacity at constant pressure is (Take gas constant R=8.3${ JK }^{ -1 }{ mol }^{ -1 }$)

  1. $8.5{ JK }^{ -1 }{ mol }^{ -1 }$
  2. $8.0{ JK }^{ -1 }{ mol }^{ -1 }$
  3. $7.5{ JK }^{ -1 }{ mol }^{ -1 }$
  4. $7.0{ JK }^{ -1 }{ mol }^{ -1 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

When an ideal diatomic gas is heated at a constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

  1. $\dfrac {2}{5}$
  2. $\dfrac {3}{5}$
  3. $\dfrac {3}{7}$
  4. $\dfrac {5}{7}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$Th\quad fraction\quad is\quad \frac { \triangle V }{ \triangle Q } \quad =\quad \frac { { _{ n }{ C } _{ v } }\triangle T }{ { _{ n }{ C } _{ p } }\triangle T } \ \frac { \triangle V }{ \triangle Q } =\frac { { C } _{ V } }{ { C } _{ P } } \quad =\quad \frac { 1 }{ Y } \ as\quad we\quad know\quad y\quad =\quad { C } _{ P }/{ C } _{ V }\ y\quad for\quad diatomatic\quad gas\quad :\quad \ { C } _{ P }\quad of\quad diatometic\quad gas\quad :\quad \frac { 7 }{ 2 } \ { C } _{ V }\quad of\quad diatometic\quad gas\quad :\quad \frac { 5 }{ 2 } \ y\quad =\quad \frac { { C } _{ P } }{ { C } _{ V } } =\frac { 7/2 }{ 5/2 } =\frac { 7 }{ 5 } \ \frac { \triangle V }{ \triangle Q } =\frac { 1 }{ y } =\frac { 1 }{ 7/5 } =\frac { 5 }{ 7 } \quad (D)$

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

For an ideal gas, the heat capacity at constant pressure is larger than that at constant volume because

  1. positive work is done during expansion of the gas by the external pressure

  2. positive work is done during expansion by the gas against external pressure

  3. positive work is done during expansion by the gas against intermolecular forces of attraction

  4. more collisions occur per unit time when volume is kept constant
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When  heat  is  supplied  at  constant  volume,  temperature  increases accordingly  to  the  ideal  gas  equation.

$P=\dfrac { nRT }{ V } $

as  V  is  constant  and  T  is  increasing,  pressure  will  also  increase.

Than at constant pressure  as temperature is increase volume increases, resulting in expansion of the gas, resulting in positive work, Hence the heat given is used up for expansion and then to increases the internal energy . The heat capacity at constant pressure is larger.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

If 'v' is the velocity of sound in a gas then 'v' is directly proportional to (where M, d and T represents molecular weight of gas, density of gas and its temperature respectively.)

  1. $\sqrt{M}$
  2. $\displaystyle \frac{1}{\sqrt{d}}$
  3. $\sqrt{T}$

  4. Both (2) and (3)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The speed of sound in a gas is given by v = sqrt(gamma * P / d) or v = sqrt(gamma * R * T / M). Since P/d = RT/M, v is proportional to sqrt(T) and inversely proportional to sqrt(M) or sqrt(d). Thus, both options 2 and 3 are correct.

Multiple choice

The amount of mass in a given volume is

  1. Pressure

  2. Volume

  3. Mass

  4. Density
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Density is a fundamental physical property defined as mass per unit volume. It measures how tightly packed the matter in an object or substance is.