Work Done in ...

Work Done in Isothermal Reversible Process

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Q. Two moles of an ideal gas initially at

27^{0} C

and one atmospheric pressure are compressed isothermally and reversibly till the final pressure of the gas is

10 a t m

. Calculate

q

for the process.

$11488 J$
$- 11488 J$
$12000 J$
$- 12000 J$

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Q. A given mass of gas expands reversibly from state A to state B by three paths 1, 2 and 3 as shown in the figure. If

w_{1}, w_{2}, a n d w_{3}

respectively are the work done by the gas along three paths, then:

$w_{1} < w_{2} > w_{3}$
$w_{1} < w_{2} < w_{3}$
$w_{1} > w_{2} > w_{3}$
$w_{1} = w_{2} = w_{3}$

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Q. Which of the following is CORRECT regarding work in reversible isothermal compression?

It is independent of volume of gas.
It depends on number of moles of gas.
It is independent of temperature of gas.
All of the above

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Q. For the cyclic process in the figure , which of the following is(are) correct :

$w_{A B} = 0$ and $w_{B C} < 0$
$w_{B C} > 0$ and $w_{C A} > 0$
$w_{c y c l i c} > 0$
$w_{B C} < 0$ and $w_{C A} > 0$

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Q. Calculate

q

(in joules), for the reversible isothermal expansion of one mole of an ideal gas

27^{o} C

from a volume of 10

d m^{3}

to a volume of

20 d m^{3}

1729 J
1504 J
1432 J
1830 J

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When the total energy change in an isothermal cycle is zero, it represents

a reversible cycle
an adiabatic change
a thermodynamic equilibrium
an irreversible cycle

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Q. How much work in

k J m o l^{- 1}

unit is done by reversible and isothermal expansion of

1.2

mole of an ideal gas to

10

times of its original volume at

27^{o} C

$4.191$
$6.892$
$- 6.892$
$- 4.191$

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Q. Calculate the work done when

2 m o l e s

of hydrogen expand isothermally and reversibly at

25^{\circ} C

from

15 t o 45 l i t r e s

$- 1309 c a l o r i e s$
$- 14.36 c a l o r i e s$
$- 2872 c a l o r i e s$
$- 28.72 c a l o r i e s$

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Q. Consider an ideal gas that occupies 2.50

d m^{3}

at a pressure of 3 bar. If the gas is compressed isothermally at a constant pressure

P_{e x t}

, so that the final volume becomes 0.5

d m^{3}

. Calculate the value of

P_{e x t}

and the work done respectively.
Given:

1 b a r . L

= 100

J

$20 b a r$ and $1000 J$
$15 b a r$ and $3000 J$
$30 b a r$ and $1500 J$
$10 b a r$ and $3750 J$

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Q. One mole of an ideal gas at 300 K is expanded isothermally from an initial volume of 1 litre to 10 litres. The value of

△ U

for this process is:

(R = 2 c a l m o l^{- 1} K^{- l})

163.7 cal
zero
138.1 cal
9 atm L

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Q. Calculate the heat involved in a reaction for the isothermal expansion of one mole of a ideal gas at

27^{o}

C from a volume of 50 L to 100 L.

$Q$ = 159 J
$Q$ = 2294 J
$Q$ = 1729 J
$Q$ = 2197 J

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Q. How much work in

k J m o l^{- 1}

unit is done by reversible and isothermal expansion of

1.2

mole of an ideal gas to

10

times of its original volume at

27^{o} C

$4.191$
$6.892$
$- 6.892$
$- 4.191$

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Q. Calculate the magnitude of maximum work done (in

J

) in expanding 16 g of oxygen at 300 K and occupying a volume of

5 d m^{3}

isothermally untill the volume becomes

25 d m^{3}

.
(Given

l o g 5 = 0.6989

)

2159 J
2007 J
1055 J
2536 J

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Q. The work done by 2 mole of an ideal gas at 300 K in a reversible isothermal expansion from 10 litres to 20 litres is

– 3458 J
+ 3458 J
– 1730 .4 J
+ 1730.4 J

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Q. Which of the following is CORRECT regarding work in reversible isothermal compression?

It is independent of volume of gas.
It depends on number of moles of gas.
It is independent of temperature of gas.
All of the above

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Q. A reversible cyclic process for an ideal gas is shown below. Here, P, V and T are pressure, volume and temperature, respectively. The thermodrynamic parameteres q, w and U are heat, work and internal energy respectively.

The incorect option(s) is(are):

$w_{A B} = - P_{2} (V_{2} - V_{1})$
$w_{B C} = - P_{2} (V_{2} - V_{1})$
$Δ U_{A B} = 0$ , $Δ U_{C A} = q_{C A}$
$w_{C A} = 0$

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Q. The work done by

200 c a l o r i e

of heat in isothermal expansion of ideal gas is:

$- 836.8 J$
$- 418.4 J$
$- 555.2 J$
$664.5 J$

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Q. A given mass of gas expands reversibly from state A to state B by three paths 1, 2 and 3 as shown in the figure. If

w_{1}, w_{2}, a n d w_{3}

respectively are the work done by the gas along three paths, then:

$w_{1} < w_{2} > w_{3}$
$w_{1} < w_{2} < w_{3}$
$w_{1} > w_{2} > w_{3}$
$w_{1} = w_{2} = w_{3}$

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Q. Calculate

q

(in joules), for the reversible isothermal expansion of one mole of an ideal gas

27^{o} C

from a volume of 10

d m^{3}

to a volume of

20 d m^{3}

1729 J
1504 J
1432 J
1830 J

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Q. The work done in erg for the reversible expansion of

1 m o l e

of an ideal gas from a volume of

10 l i t r e s

20 l i t r e s

25^{o} C

$2.303 \times 298 \times 0.082 l o g 2$
$- 298 \times 10^{7} \times 8.314 \times 2.303 l o g 2$
$- 2.303 \times 298 \times 0.082 l o g 0.5$
$2.303 \times 298 \times 2 l o g 2$

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Q. 5 moles of an ideal gas at

27^{\circ} C

expands isothermally and reversibly from a volume of 6 L to 60 L. The work done in kJ is:

-28.72 kJ
-32.60 kJ
14.28 kJ
20.32 kJ

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Q. Calculate the work done by

10 g

of an ideal gas of molecular weight

44

in expanding reversibly and isothermally from a volume of

5

10

litre at

300 K

$93.93 c a l$
$- 63.63 c a l$
$- 93.93 c a l$
$63.63 c a l$

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Q. One mole of an Ideal gas was compressed isothermally and reversibly from

22.4 \times 10^{- 3} m^{3}

and one atmospheric pressure to

11.2 \times 10^{- 3} m^{3} (R = 8.314 J / K / m o l)

. The work done on the system is

- 1134 J
1134 J
1573 J
Cannot be caluclated

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Q. An ideal gas is allowed to expand against a constant pressure of

2 b a r

from

10 L t o 50 L

in one step. Calculate the magnitude of work done by the gas. If the same expansion were carried out reversibly, will the magnitude work done be higher or lower than the earlier case? (Given that,

1 L b a r = 100 J

)

$8 k J$ , higher
$- 8 k J$ , higher
$- 8 k J$ , lower
$8 k J$ , lower

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Q. A given mass of gas expands from state A to state B by three paths 1, 2 and 3 as shown in the figure below, If

w_{1}, w_{2}

and

w_{3}

respectively, be the work done by the gas along three paths, then

$w_{1} > w_{2} > w_{3}$
$w_{1} < w_{2} < w_{3}$
$w_{1} = w_{2} = w_{3}$
$w_{1} < w_{2}; w_{1} < w_{3}$

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Q. The plots which does not represent isothermal expansion of an ideal gas is:

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Q. One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is

W_{s}

and that along the dotted line path is

W_{d}

then the integer closest to the ratio

\frac{W_{d}}{W_{s}}

is:___

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10 mole of ideal gas expands isothermally and reversibly from a pressure of 10 atm to 1 atm at 300 K. What is the heavisest mass which can lifted through a height of 100 meter by this gas?

31842 kg
58.55 kg
342.58 kg
None of these

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Q. Calculate the magnitude of maximum work done (in

k J

) in expanding 6 g of hydrogen at 300 K and occupying a volume of

10 d m^{3}

isothermally untill the volume becomes

30 d m^{3}

.
(Given

l o g 5 = 0.6989

)

7886 J
4521 J
8221 J
1005 J

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Q. Carbon monoxide is allowed to expand isothermally and reversibly from

10 m^{3} t o 20 m^{3}

300 K

and work obtained is

4.754 k J

. Calculate the number of moles of carbon monoxide

$27.5 m o l$
$5.5 m o l$
$2.75 m o l$
$55.0 m o l$

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