Question

A diatomic ideal gas initially at pressure 3 atm and volume 2 L expands adiabatically to a volume of 8 L. How much work is done by the gas during the expansion? a)599 J b)540 J c)466 J d) 647 J (e) 782 J

Answer 1

option d is correct

work done is 647 J

Step-by-step explanation:

Given data

pressure P = 3 atm

volume V1 = 2 L

volume V2 = 8 L

to find out

work is done by the gas

solution

we know that work done formula that is

work done = k (
`V_(f)^(n)` -
`V_(i)^(n)` ) / n

here n = 1 - γ

and k = PV^γ

and we know for diatomic gas γ = 1.4

so k will be = ( 3× 101325 ) ×
`(0.002)^(1.4)`

k = 50.62

so that now

work done = k (
`V_(f)^(n)` -
`V_(i)^(n)` ) / n

work done = 50.62 (
`(0.008)^(1-1.4)` -
`(0.002)^(1-1.4)` ) / 1-1.4

so work done will be 647 J

so option d is correct

work done is 647 J