How would you calculate the work associated with the compression of a gas from 121.0 L to 80.0 L at a pressure of 13.1 atm?

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Answer 1 · 2017-09-30T23:54:40

#W_"on gas"~~1.75xx10^5" J"#

Assuming this is an ideal gas:

#W_"env"=-int_(v_i)^(v_f)" P dV"#

#=>W_"env"=-PDeltaV=P(V_"f"-V_"i")#

Let's convert liters to cubic meters first so that our units work out.

#=>V_"i"=0.212" m"^3#

#=>V_"f"=0.08" m"^3#

We also know that #P=13.1" atm"#, which is #1327358 " N"//"m"^2#.

#=>W_"env"=-(1327358 " N"//"m"^2*(0.08" m"^3-0.212" m"^3))#

#=>=-(1327358 " N"//"m"^2*-0.132" m"^3)#

#=>~~1.75xx10^5" Nm"#

#=>~~color(blue)(1.75xx10^5" J")#

#:.# The work done on the gas by the environment to compress the gas is #~~1.75xx10^5" J"#