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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 (i) the final temperature of the gas and (ii) 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) -57 kJ

Text Solution

Verified by Experts

The correct Answer is:
A
`T_1V_(1)^(r-1)=T_2V_(2)^(r-1)" "gamma=(5)/(3)`
`implies 300(V)^(2/3)= T_2(2V)^(2/3) implies 300(V)^(2/3)= T_2(2V)^(2/3)`
`implies T_2=(300)/(2^(2/3))approx 189K, " " triangleU=(f)/(2)nRTtriangleT`
`=(3)/(2)*2(25)/(2)(189-300) ," "= -2.7KJ`.
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