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Answer 1 · 2017-05-28T15:02:26

#sf(1.7xx10^(10)color(white)(x)"erg")#

The work done in expanding the gas at constant temperature is given by:

#sf(W=int_(v_i)^(v_f)P.dV)#

Since #sf(PV=nRT)# then #sf(P=(nRT)/V)#

#:.##sf(W=nRTint_(v_i)^(v_f)(dV)/V)#

Integrating and putting in the limits gives:

#sf(W=nRTln[V_(f)/V_(I)])#

Putting in the numbers:

#sf(W=1xx8.31xx298xxln[20/10]color(white)(x)J)#

#sf(W=1xx8.31xx298xx0.693color(white)(x)J)#

#sf(W=1716.5color(white)(x)J)#

For some reason you have asked for the answer to be in "ergs". This is an obsolete, non SI unit. 1 Joule = #sf(10^7)# erg so:

#sf(W=1.7xx10^(10)color(white)(x)"erg")#