Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Column- I Column –II A) An insulated container has two chambers separated by a valve. Chamber I contains an ideal gas and the Chamber II has vacuum. The valve is opened p) The temperature of the gas decreases B) An ideal monoatomic gas expands to twice its remains original volume such that its pressure P ∞ 1/V^2 where V is the volume of the gas q) The temperature of the gas increases or constant C) An ideal monoatomic gas expands to twice its original volume such that its pressure P ∞ 1/V^{4\/3} r) The gas loses heat where Vis its volume D) An ideal monoatomic gas expands such that its pressure P and volume V follows the behaviour shown in the graph s) The gas gains heat

Correct Answer is : A → q ;B → p,r; C → p, s; D → q, s

A → q ;B → p,r; C → p, s; D → q, s

A → p,r ; B → p, s ; C → q, s ; D → q

A → p,a ; B → q , s ; C → q ; D → p

A → q, s ; B → q ; C → p, r ; D → p, s

JEE Advanced Model Paper 6 with solutions for online practice

Question : 17 of 60

Marks: +1, -0

Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process.

Column- I	Column –II
A) An insulated container has two chambers separated by a valve. Chamber I contains an ideal gas and the Chamber II has vacuum. The valve is opened	p) The temperature of the gas decreases
B) An ideal monoatomic gas expands to twice its remains original volume such that its pressure P ∞ 1/V2 where V is the volume of the gas	q) The temperature of the gas increases or constant
C) An ideal monoatomic gas expands to twice its original volume such that its pressure P ∞ 1/V4∕3	r) The gas loses heat where Vis its volume
D) An ideal monoatomic gas expands such that its pressure P and volume V follows the behaviour shown in the graph	s) The gas gains heat

A → q ;B → p,r; C → p, s; D → q, s
A → p,r ; B → p, s ; C → q, s ; D → q
A → p,a ; B → q , s ; C → q ; D → p
A → q, s ; B → q ; C → p, r ; D → p, s

Validate

Solution:

A) As the ideal gas expands in vacuum, no work is done (W = 0). Also the container isinsulated therefore no heat is lost or gained (Q = 0). According to first law ofthermodynamicsΔU = Q + W
∴ ΔU = 0 ⇒ There is no change in the temperature of the gas
B) Given PV2 = constant ..... (i)
Also for an ideal gas

= constant
From (i) & (ii) V × T = constantAs the gas expands its volume increases and temperature decreases∴ (p) is the correct option
To find whether heat is released or absorbed let us find a relationship between Q and
change in temperature ΔT
We know that Q = nCΔT ..... (i)
Where C = molar specific heat
Also for a polytripic process we have
C = Cv +

1−n

and PVn = constant
Here PV2 = Constant. Therefore n =2
∴ C = Cv +

1−2

= Cv - R
For mono atomic gas
Cv =

R
∴ C =

R - R =

Substituting this value in (1) we get
Q = n ×

× ΔT
In this case the temperature decreases i.e. ΔT is negative. Therefore Q is negative. Thisin turn means that heat is lost by the gas during the process. (r ) is the correct option.
C) Proceeding in the same way we get in this case V1∕3 × T = constant
⇒ As the gas expands and volume increases, the temperature decreases. Therefore (p) isthe correct option
In this process, x =

∴ C = Cv +

1−

R +

−1

R - 3R =

−3R

∴ Q = n (

−3R

)Δt
As ΔT is negative, Q is positive. This in turn means that heat is gained by the gas duringthe process (s) is the correct option
D) Also ΔT =

Δ(PV)

Here Δ(PV) is posiitve ∴ ΔT is posiitve ∴ temperature increase increases(q) is thecorrect option From the graph it is clear that during the process the pressure of the gasincreases which shows that the internal energy of the gas has increased. Also the volumeincreases which means work is done by the system which needs energy. From these twointerpretation we can comfortably conclude that the gas gains heat during the process.(s) is the correct option.

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