Tag: work done by an ideal gas in isothermal expansion

Questions Related to work done by an ideal gas in isothermal expansion

The work done by 100 calorie of heat in isothermal expansion of ideal gas is 

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. 418.4J

  2. 4.184J

  3. 41.84J

  4. None

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Correct Option: A
Explanation:

One calorie is equivalent to $4.184$ joules 

or,   $J=4.18 J/cal$.
Work done (W)=$ = 4.18 \times 500 = 2090\,J$
As $1$ calorie is equal to $4.184$ calorie then $100$ calorie is equal to $ = 4.184 \times 100 = 418.4$

Work done during isothermal expansion depends on change in

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. volume

  2. pressure

  3. both (a) and (b)

  4. none of these

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Correct Option: C
Explanation:

Work done in isothermal expansion is given as $W=nRT\ln(\displaystyle\frac{V _f}{V _i})=nRT\ln(\frac{P _i}{P _f})$. Thus it depends both on pressure and volume.

Expansion of 1 mole of ideal gas is taking place from 2 litres to 8 litres at 
300 K against 1 atm pressure. calculate $ \Delta JK^{-1} mol^{-1} $ given $ R= \dfrac {8.3J}{mol-K}, 1 lit-atm= 100 j,in 2=0.693) $

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. $11.5$

  2. $13.5$

  3. $9.5$

  4. $22.5$

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Correct Option: B

The pressure and volume of a given mass of gas at a given temperature are $ \mathrm{P}  $ and $ \mathrm{V}  $ respectively.Keeping temperature constant, the pressure is increased by 10$  \%  $ and then decreased by 10$  \%  $ .The volume how will be -

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. less than $ \mathrm{V} $

  2. more than $ \mathrm{V} $

  3. equal to $ \mathrm{V} $

  4. less than $ V $ for diatomic and more than $ V $ for monoatomic

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Correct Option: C

Two bulbs of volume V and 4V contains gas at pressures of 5 atm,. 1 atm and at temperatures of 300K and 400K respectively. When these bulbs are joined by narrow tube keeping their temperature at their initial values. The pressure of the system is

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. 1 atm

  2. 2 atm

  3. 2.5 atm

  4. 3 atm

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Correct Option: A

In isobaric process of ideal gas $(f = 5)$ work done by gas is equal to $10\ J$. Then heat given to gas during process is

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. $25\ J$

  2. $15\ J$

  3. $45\ J$

  4. $35\ J$

Show answer
Correct Option: D
Explanation:

$\triangle Q = \left (\dfrac {f}{2} + 1\right ) nR\triangle T = \dfrac {7}{2} \times 10 = 35\ J$.

One mole of an ideal gas at $300K$ is expanded isothermally from an initial volume of $1litre$ to $10litres$. The $\Delta E$ for this process is $(R=2cal.mol-1K-1)$

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. $1381.1cal$

  2. zero

  3. $163.7cal$

  4. $9lit.atm$

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Correct Option: B

An Ideal gas undergoes an isobaric process. If its heat capacity is $C _v$ at constant volume and number of mole $n$. then the ratio of work done by gas to heat given to gas when temperature of gas changes by $\Delta T$ is:

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. $\left(\dfrac{nR}{c _v + R}\right)$

  2. $\left(\dfrac{R}{c _v + R}\right)$

  3. $\left(\dfrac{nR}{c _v - R}\right)$

  4. $\left(\dfrac{R}{c _v - R}\right)$

Show answer
Correct Option: A
Explanation:

$\dfrac{f}{2} R = \dfrac{C _v}{n}$
$W = nR \Delta T$
$\Delta Q = \left(\dfrac{f}{2} + 1\right) nR \, \Delta T$
$\dfrac{W}{\Delta Q} = \left(\dfrac{2}{f + 2} \right) = \dfrac{2}{\dfrac{2C _v}{nR} + 2} = \left(\dfrac{nR}{C _v + R} \right)$

Three moles of an ideal gas kept at a constant temperature at $300 K$ are compressed from a volume of $4 L$ to $1 L$. The work done in the process is

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. $-10368 J$

  2. $-110368 J$

  3. $12000 J$

  4. $120368 J$

Show answer
Correct Option: A
Explanation:

Work done in an isothermal process is given by 
$\displaystyle{W = 2.3026nRT\log _{10}\frac{V _2}{V _1}}$
Here, $n = 3, R = 8.31 J/mol^oC$
$T = 300 K$, $V _1= 4 L$, $V _2 = 1 L$
Hence, $\displaystyle{W = 2.3026 \times 3 \times 8.31 \times 300 \times log _{10}\frac{1}{4}}$
= $17221.15 (-2\log _{10} 2$)
= $-17221.15 \times 2 \times 0.3010 = -10368J$ 

A physical quantity that is conserved in a process

physics isothermal and adiabatic processes work done by an ideal gas in isothermal expansion thermodynamic processes heat and thermodynamics

  1. must have the same value for all observers

  2. can never take negative values

  3. must be dimensionless

  4. need not necessarily be a scalar

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Correct Option: A