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Two moles of an ideal monatomic gas occu...

Two moles of an ideal monatomic gas occupies a volume V at `27^(@)C`. The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b) change in its internal energy

A

(a) 189 K (b) -2.7 kJ

B

(a) 195 K (b) 2.7 kJ

C

(a) 189 K (b) 2.7 kJ

D

(a) 195 K (b) -2.7 kJ

Text Solution

Verified by Experts

The correct Answer is:
A
In adiabatic process, `TV^(gamma - 1)` = constant
So, `T_(i)V_(i)^(gamma - 1) = T_(f)V_(f)^(gamma - 1)`
or, `T_(f) = T_(i)((V_i)/(V_f))^(gamma - 1) = 300(V/(2V))^(5/3-1)`
[for monatomic gas `gamma = 5/3]`
`= 1.8898 = 189 K`
Change in internal energy
`Delta U = nC_(v)Delta T = 2 xx (3R)/2 xx (189 - 300)`
`= -2700 J = -2.7 kJ`.
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