Question 1

An ideal gas has initial volume V and pressure P. In doubling its volume the minimum work done will be in the following process(of given processes)

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

Isobaric process
Isothermal process
Adiabatic process
None of the above.

Answer

Correct Option: C

Question 2

Two difference gases of molecular masses $M _1$ and $M _2$ are at the same temperature. What is the ratio of their mean square speeds?

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

$\dfrac{M _1}{M _2}$
$\dfrac{M _2}{M _1}$
$\sqrt {\dfrac{M _1}{M _2}}$
$\sqrt {\dfrac{M _2}{M _1}}$

Answer

Correct Option: A

Question 3

A diatomic gas which has initial volume of $10$ litre is isothermally compressed to $1/15^{th}$ of its original volume where initial pressure is $10^5$ Pascal. If temperature is $27^o$C then find the work done by gas.

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

$-2.70\times 10^3$J
$2.70\times 10^3$J
$-1.35\times 10^3$J
$1.35\times 10^3$J

Answer

Correct Option: A

Question 4

One mole of an ideal gas undergoes an isothermal change at temperature T so that its volume V is doubled. R is the molar gas constant. Work done by the gas during this change is :

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

RT $\ln 4$
RT $\ln 3$
RT $ \ln 2$
RT $ \ln 1$

Answer

Correct Option: C

Question 5

The slope of adiabatic curve is ________ than the slope of an isothermal curve.

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

Greater.
lesser
data insufficient
can be both a and b

Answer

Correct Option: A

Question 6

Three moles of an ideal gas $\left (C _{P} = \dfrac {7R}{2}\right )$ at pressure $P _{A}$ and temperature $T _{A}$ is isothermally expanded to twice the initial volume. The gas is then compressed at constant pressure to its original volume. Finally the gas is heated at constant volume to its original pressure $P _{A}$.
Calculate the net work done by the gas and the net heat supplied to the gas during the complete process.

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

$0.579\ RT _{A}, \triangle Q = 0.579\ RT _{A}$.
$79\ RT _{A}, \triangle Q = 0.679\ RT _{A}$.
$0.9\ RT _{A}, \triangle Q = 0.779\ RT _{A}$.
$0.7\ RT _{A}, \triangle Q = 0.979\ RT _{A}$.

Answer

Correct Option: A

Question 7

Two soap bubbles having radii $3\ cm$ and $4\ cm$ in vacuum, coalesce under isothermal conditions. The radius of the new bubble is

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

$1\ cm$
$5\ cm$
$7\ cm$
$3.5\ cm$

Answer

Correct Option: B

Question 8

One mole of an ideal gas u ndergoes a process:
$P = \dfrac{P _0}{1+(V _0/ V)^2}$.
Here $P _0$ and $V _0$ are constants. change in temperature of the gas when volume is changed from $V=V _0$ to $V = 2V _0$ is:

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

$-\dfrac{2P _0V _0}{5R}$
$\dfrac{11P _0V _0}{10R}$
$-\dfrac{5P _0V _0}{4R}$
$P _0V _0$

Answer

Correct Option: B

Question 9

Let $Q$ and $W$ denote the amount of heat given to an ideal gas and the work done by it in an isothermal process.

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

$Q = 0$
$W = 0$
$Q \neq W$
$Q = W$

Answer

Correct Option: D

Question 10

Work done during isothermal expansion of one mole of an ideal gas $10$ atm to $1$ atm at $300\ K$ is

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

$-4938.8\ J$
$4938.8\ J$
$-5744\ J$
$6257.2\ J$

Answer

Correct Option: C

Question 11

Identical cylinders contain helium at 2.5 atm and agron at 1 atm respectively. If the are filled in one of the cylinder,the pressure would be.

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

3.6 atm
1.75 atm
1.5 atm
1.0 atm

Answer

Correct Option: B

Question 12

One mole of an ideal monoatomic gas is at $360K$ and a pressure of $10 ^ { 5 } Pa.$ It is compressed at constant pressure until its volume is halved. Taking $R$ as $8.3 J{ mol } ^ { - 1 }{ K } ^ { - 1 }$ and the initial volume of the gas as $3.0 \times 10 ^ { - 2 } { m } ^ { 3 }$ , the work done on the gas is

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

$-1500 J$
$+1500 J$
$-3000 J$
$+3000 J$

Answer

Correct Option: A

Question 13

An ideal gas is taken from state $A$ (pressure $P$, volume $V$) to state $B$ (pressure $\displaystyle\frac{P}{2}$, volume $2V$) along a straight line path in the pressure-volume diagram. Select the correct statements from the following.

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

The work done by the gas in the process $A$ to $B$ exceeds the work done that would be done by it if the system were taken from $A$ to $B$ along an isotherm.
In the temperature-volume diagram, the path $AB$ becomes a part of a parabola.
In the pressure-temperature diagram, the path $AB$ becomes a part of hyperbola.
In going from $A$ to $B$, the temperature $T$ of the gas first increases to a maximum value and then decreases.

Answer

Correct Option: A,B,D

Question 14

A fixed mass of a gas is first heated isobarically to double the volume and then cooled isochorically to decrease the temperature back to the initial value. By what factor would the work done by the gas decreased, had the process been isothermal?

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

$2$
$\displaystyle\dfrac{1}{2}$
$\ln 2$
$\ln 3$

Answer

Correct Option: C

Question 15

Work done in reversible isothermal process by an ideal gas is given by

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

$2.303 \text { nRT log } \frac { V _ { 2 } } { V _ { 1 } }$
$\frac { n R } { ( y - 1 ) } \left( T _ { 2 } - T _ { 1 } \right)$
$2.303 \text { nRT log } \frac { V _ { 1 } } { V _ { 2 } }$
None

Answer

Correct Option: A

Question 16

$0\cdot 5\ mole$ of oxygen and $0\cdot 5\ mole$ of nitrogen, each having $V$ and temperature $T$ are mixed isothermally to have the total volume $2\ V$. The maximum work done is :

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

$RT\ \log _{e}2\ joule$
$\dfrac {RT}{2}\ \log _{e}2\ joule$
$RT\ (\log _{e}4)\ joule$
$zero$

Answer

Correct Option: C

Question 17

A gas expands from $1l$ to $3l$ at atmospheric pressure. The work done by the gas is about

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

$2\ J$
$200\ J$
$300\ J$
$2 \times 10^{5}\ J$

Answer

Correct Option: B

Question 18

4 atm pressure to attain 1 atm pressure by result of isothermal expansion. The work done by the gas during expansion is nearly.

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

155 J
255 J
355 J
555 J

Answer

Correct Option: D

Question 19

During the process A -B of an ideal gas:

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

work done on the gas is zero
density of the gas is constant
slope of line AB from the T - axis is inversely proportional to the number of moles of the gas
slope of line AB from the T - axis is directly proportional to the number of moles of the gas

Answer

Correct Option: A

Question 20

A gas follow a general process as $PV RT + 3V$ for $1\ mole$ of gas. If it expands isobarically till temperature is doubled, then the work done by the gas is (initial temperature and pressure are $T _{0}$ and $P _{0}$ respectively).

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

$\dfrac {P _{0}T _{0}R}{(2P _{0} - 3)}$
$\dfrac {P _{0}T _{0}R}{(P _{0} - 3)}$
$\dfrac {P _{0}T _{0}R}{(P _{0}V - 3)}$
$\dfrac {3P _{0}V _{0}}{R}$

Answer

Correct Option: A

Question 21

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

418.4J
4.184J
41.84J
None

Answer

Correct Option: A

Question 22

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

volume
pressure
both (a) and (b)
none of these

Answer

Correct Option: C

Question 23

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

$11.5$
$13.5$
$9.5$
$22.5$

Answer

Correct Option: B

Question 24

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

less than $ \mathrm{V} $
more than $ \mathrm{V} $
equal to $ \mathrm{V} $
less than $ V $ for diatomic and more than $ V $ for monoatomic

Answer

Correct Option: C

Question 25

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 atm
2 atm
2.5 atm
3 atm

Answer

Correct Option: A

Question 26

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

$25\ J$
$15\ J$
$45\ J$
$35\ J$

Answer

Correct Option: D

Question 27

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

$1381.1cal$
zero
$163.7cal$
$9lit.atm$

Answer

Correct Option: B

Question 28

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

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

Answer

Correct Option: A

Question 29

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

$-10368 J$
$-110368 J$
$12000 J$
$120368 J$

Answer

Correct Option: A

Question 30

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

must have the same value for all observers
can never take negative values
must be dimensionless
need not necessarily be a scalar

Answer

Correct Option: A

Question 31

For an isothermal expansion of an ideal gas, mark wrong statement

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

there is no change in the temperature of the gas
there is no change in the internal energy of the gas
the work done by the gas is equal to the heat supplied to the gas
the work done by the gas is equal to the change in its internal energy

Answer

Correct Option: D

Question 32

If a given mass of gas occupies a volume of 10 cc at 1 atmospheric pressure and temperature 100$^o$C. What will be its volume at 4 atmospheric pressure, the temperature being the same?

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

100 cc
400 cc
1.04 cc
2.5 cc

Answer

Correct Option: D

Question 33

The cyclic process from X to Y is an isothermal process.
If the pressure of the gas at X is 4.0 kPa, and the volume is 6.0 cubic meters, and if the pressure at Y is 8.0 kPa, what is the volume of the gas at Y?

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

12.0 cubic meters
16.0 cubic meters
3.0 cubic meters
4.0 cubic meters
2.0 cubic meters

Answer

Correct Option: C

Question 34

The work done y a gas is an isothermal change where 1 refers to initial state and 2 refers to final state is

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

$\mu R({T _2} - {T _1})\ln \left( {\frac{{{V _2}}}{{{V _1}}}} \right)$
$\mu R{T _1}\ln \left( {\frac{{{V _2}}}{{{V _1}}}} \right)$
$\mu R{T _2}\ln \left( {\frac{{{V _1}}}{{{V _2}}}} \right)$
$\mu R\left( {\frac{{{T _1} + {T _2}}}{2}} \right)[\ln {V _2} - \ln {V _1}]$

Answer

Correct Option: B

Question 35

A thin tube of uniform cross-section is sealed at both ends. When it lies horizontally, the middle $5$cm length contains mercury and the two equal ends contain air at the same pressure P. When the tube is held at an angle of $60^o$ with the vertical, then the lengths of the air columns above and below the mercury column are $46$cm and $44.5$cm respectively. Calculate the pressure P in cm of mercury. The temperature of the system is kept at $30^o$C.

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

$75.4$
$45.8$
$67.5$
$89.3$

Answer

Correct Option: A

Question 36

An ideal gas system undergoes an isothermal process, then the work done during the process is:

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

$nRT ln\dfrac { { V } _{ 2 }}{ { V } _{ 1 } }$
$nRT ln\dfrac { { V } _{ 1 }}{ { V } _{ 2 }}$
$2nRT ln\dfrac { { V } _{ 2 }}{ { V } _{ 1 }}$
$2nRT ln\dfrac { { V } _{ 1 }}{ { V } _{ 2 }}$

Answer

Correct Option: A

Question 37

A vertical cyclinder with heat - conducting with heat conducting walls is closed at the bottom and its fitted with a smooth light piston. It contains one mole of an ideal gas. The temperature of the gas is always equal to the surrounding's temperature $T _o$ . The piston is moved up slowly to increase the volume of the gas to $n$ times. Which of the following is incorrect?

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

Work done by the gas in $RT _o\ln (n)$.
Work done against the atmosphere is $RT _o(n-1).$
There is no change in the internal energy of the gas.
The final presure of the gas is $\dfrac{1}{n-1}$ times its initial pressure.

Answer

Correct Option: D

Question 38

Two moles of a gas is expanded to double its volume by two different processors. One is isobaric and the other is isothermal. If ${w} _{1}$ and ${w} _{2}$ are the works done respectively, then

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

${ w } _{ 2 }=\cfrac { { w } _{ 1 } }{ \ln { 2 } } $
${ w } _{ 2 }={ w } _{ 1 }$
${ w } _{ 2 }={ w } _{ 1 }\ln { 2 } $
${ w } _{ 1 }^{ 2 }={ w } _{ 2 }\ln { 2 } $

Answer

Correct Option: C

Question 39

Let $ \triangle W _a and \triangle W _b $ the work done by the system A and B respectively in the previous question

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

$ \triangle W _a > \triangle W _b $
$ \triangle W _a = \triangle _b $
$ \triangle W _a < \triangle W _b $
The relation between $ \triangle W _a and \triangle W _b $ cannot be deduced.

Answer

Correct Option: C

Description: work done by an ideal gas in isothermal expansion
Number of Questions: 39
Created by: Gagan Singh
Tags: thermodynamics isothermal and adiabatic processes heat and thermodynamics physics

Work done by an ideal gas in isothermal expansion - class-XI

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