Nitrogen gas of 0.014 kg mass at 27 °C is
filled in a container. How much amount of
heat is required to double the root mean square
velocity of molecules? (kb= 1.38x10-2JK and
N=6x102(kg mol)-1). [Ans- 9315 J]
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ANSWER
As gas is enclosed in the cylinder, V=constant
(ΔQ)
v
=μC
v
ΔT
Here, μ=
28
0.014×10
3
=
2
1
mol
And as nitrogen is diatomic, C
v
=
2
5
R,
Further, as according to the given problem,
(v
rms
)
1
(v
rms
)
2
=
T
1
T
2
=2, i.e., T
2
=4T
1
ΔT=4T
1
−T
1
=3T
1
=3×300=900K
(ΔQ)
v
=
2
1
×
2
5
×2×900=2250cal
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