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Work Done in ...

Work Done in Isothermal Reversible Process

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Q.

Match gases under specified conditions listed in Column 1 with their properties/laws in Column II.

$\begin{matrix} C o l u m n I & C o l u m n I I A & H y d r o g e n g a s ⟮ p = 200 a t m, T = 273 K ⟯ & p & C o m p r e s s i o n f a c t o r = 1 B & H y d r o g e n g a s ⟮ p = 0 a t m, T = 273 K ⟯ & q & A t t r a c t i v e f o r c e s a r e d o m i n a n t C & C O_{2} ⟮ p = 1 a t m, T = 273 K ⟯ & r & p V = n R T D & R e a l g a s w i t h v e r y l a r g e m o l a r v o l u m e & s & p ⟮ V - n b ⟯ = n R T \end{matrix}$

A →(r), B →(p), C →(s), D →(q)
A →(p, s), B →(r), C →(p, q), D →(p, s)
A →(q), B →(p), C →(s), D →(r)
A →(p), B →(q), C →(r), D →(s)

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Q.

In a process a system does 140 J of work on the surrondings and only 40 J of heat is added to the system, hence change in internal energy is

180 J
-180 J
-23.92 Cal
-180 J

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Q. The total internal energy change for a reversible isothermal cycles is

Always 100 calories per degree
Always negative
\N
Always positive

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Q. Two samples A and B initially at the same temperature and pressure and compressed from volume V to V/2 ( A is isothermally and B adiabatic ally).The final pressure

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

B and D
A and D
B and C
A and C

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Q. Calculate the maximum work done (in

c a l

) when pressure on 10 gram of hydrogen is reduced from

20

to

1 a t m

at a constant temperature of

273 K

. the gas behave Ideally

$8192.6 c a l$
$9258.3 c a l$
$5924.2 c a l$
$2896.4 c a l$

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Q. Select the correct statements.
a. the magnitude of work involved in an intermediate irreversible expansion is less than involved in reversible expansion.
b. the magnitude of work involved in an intermediate reversible compression is more than that involved in intermediate irreversible compression.

Statement b
Statement a
neither a nor b
A is correct while b is incorrent
Both the statements are correct

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Q. Two moles of helium gas (

γ = 5 / 3

) are initially at a temperature of

27^{o} C

and occupy a volume of

20 l i t r e

. The gas is first expanded at constant pressure until the volume is doubled. It then undergoes adiabatic change until the temperature returns to its initial value. If total work done by the gas is

- x k c a l

, then what is

x

?

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Q. Which one of the following is correct for the isothermal expansion of an ideal gas?

U and H increases
U increases but H decreases
U and H are unchanged
H increases but U decreases

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Q. What is the relation between

C_{p}

and

C_{v}

for methanol?

$C_{p} >> C_{v}$
$C_{p} \geq C_{v}$
$C_{v} \geq C_{p}$
$C_{v} >> C_{p}$

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Q. For isothermal reversible expansion of an ideal gas:

$△ H > 0$ and $△ U = 0$
$△ H > 0$ and $△ U < 0$
$△ H = 0$ and $△ U = 0$
$△ H = 0$ and $△ U > 0$

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Q.

1

mole of an ideal gas at

25^{o} C

is allowed to expand reversible at constant temperature from a volume of

10 l i t r e

to

20 l i t r e

. Calculate the work done by the gas in joule and calorie.

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Q.

Calculate the work done for a reversible isothermal expansion of one mole of an ideal gas at $127^{\circ} C$ from a volume of $10 d m^{3}$ to $20 d m^{3}$

-2305.3 J
2305. 3 J
-2306.3 J
2306.3 J

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Q. Find the work done when

2

moles of hydrogen expands isothermally from

15

L to

50

L against a constant pressure of 1 atm at

25^{0} C

.

$820.8 c a l$
$- 848.2 c a l$
$84.7 c a l$
$- 848.2 k c a l$

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Q. A gas expands isothermally against a constant external pressure of

1 a t m

from a volume of

10 d m^{3}

to a volume of

20 d m^{3}

. It absorbs

300 J

of thermal energy from its surrounding. The

△ U

is:

$- 312 J$
$+ 123 J$
$- 213 J$
$+ 231 J$

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Q. Calculate the

Q

for the isothermal reversible expansion of 1 mole of an ideal gas from initial pressure of 1.0 bar to a final pressure 0.1 bar at a constant temperature at 273 K.

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Q. At

25^{o} C

, a

0.01

mole sample of a gas is compressed in volume from

4.0 L

to

1.0 L

at constant temperature. What is work done for this process if the external pressure is

4.0

bar?

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Q. If

W_{1}, W_{2}, W_{3}, W_{4}

for an ideal gas are magnitude of work done in isothermal, adiabatic, isobaric, isochoric reversible expansion processes, then the correct order will be (assume expansion to be from same initial points to same final volume wherever applicable)

$W_{1} > W_{2} > W_{3} > W_{4}$
$W_{3} > W_{2} > W_{1} > W_{4}$
$W_{3} > W_{2} > W_{4} > W_{1}$
$W_{3} > W_{1} > W_{2} > W_{4}$

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Q. At

27^{o}

C, one mole of an ideal gas is compressed isothermally and reversibly from a pressure of 2 atm to 10 atm.
Choose the correct option from the following:

Heat is negative
Work done is - 965.84 cal
All are incorrect
Change in internal energy is positive

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Q.

Isothermally at $27^{\circ} C$ , one mole of a vanderwaal's gas expands reversibly from 2 liters to 20 liters. Calculate the work done if $a = 1.42 \times 10^{12} d y n e s c m^{4} p e r m o l e$ and $b = 30 c . c$

- 58.12 k J
-861.2 k J
-691.2 k J
-761.2 k J

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Q. The standard state Gibbs free energies of formation of

C (g r a p h i t e)

and

C (d i a m o n d)

at T = 298 K are

Δ_{f} G^{\circ} [C (g r a p h i t e)] = 0 k J m o l^{- 1}

Δ_{f} G^{\circ} [C (d i a m o n d)] = 2.9 k J m o l^{- 1}

The standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite [C(graphite)] to diamond [C(diamond)] reduces its volume by

2 \times 10^{- 6} m^{3} m o l^{- 1}

. If

C (g r a p h i t e)

is converted to

C (d i a m o n d)

isothermally at T = 298 K, the pressure at which

C (g r a p h i t e)

is in equilibrium with

C (d i a m o n d)

is:
[Useful information:

1 J = 1 k g m^{2} s^{- 2}

;

1 P a = 1 k g m^{- 1} s^{- 2}

;

1 b a r = 10^{5} P a

]

14501 bar
58001 bar
1450 bar
29001 bar

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Q. The statement that is incorrect among the following is:

For an isothermal process, work done in reversible expansion is more than work done in irreversible expansion
For an isothermal irreversible expansion, greater the difference in initial and final pressure, lesser is the work done
For an isothermal irreversible compression, greater the difference in initial and final pressure, greater is the work done
None of the above

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Q. During isothermal expansion of one mole of an ideal gas from

10 a t m

to

1 a t m

at

273 K

, the work done is: [Gas constant =

2

]

$- 1257.43 c a l$
$- 895.8 c a l$
$- 1499.6 c a l$
$- 1172.6 c a l$

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Q.

Calculate work done when 1 mole of an ideal gas is expanded reversibly from

30 L

to

60 L

at a constant temperature of

300 K

?

$8.78 k J$
$- 1.73 k J$
$10.73 k J$
$- 9.78 k J$

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Q. In adiabatic process, the work involved during expansion or compression of an ideal gas is given by:

$n C_{v} Δ T$
$\frac{n R}{γ - 1} (T_{2} - T_{1})$
$- n R P_{e x t} [\frac{T_{2} P_{1} - T_{1} P_{2}}{P_{1} P_{2}}]$
$- 2.303 R T log \frac{V_{2}}{V_{1}}$

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Q. Calculate the amount of work done by

2

mole of an ideal gas at

298 K

in reversible expansion from

10

litre to

20

litre.

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Q. Find the work done when

2

moles of hydrogen expands isothermally from

15

L to

50

L against a constant pressure of 1 atm at

25^{0} C

.

$820.8 c a l$
$- 848.2 c a l$
$84.7 c a l$
$- 848.2 k c a l$

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Q. Calculate the work done when

1

mol of an ideal gas is compressed reversibly from

1

bar to

4

bar at a constant temperature of

300 K

:

$+ 3.45 k J$
$- 8.02 k J$
$+ 18.02 k J$
$- 14.01 k J$

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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. A

27^{\circ} C

one mole of an ideal gas is compressed isothermally and reversible from a pressure of

2 a t m

to

10 a t m

. The value of

Δ E

and

q

are

(R = 2 c a l)

:

$0, - 965.84 c a l$
$+ 965.58 c a l, - 865.58 c a l$
$- 965.84 c a l, - 865.58 c a l$
$+ 965.84 c a l, + 865.58 c a l$

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