College Physics

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7 Moles of a gas initially at temperature 300 K is compressed adiabatically from a volume of 1000 cm3 to a volume of 316 cm3.  To the nearest tenth of a kJ what is the work done by the piston? (It is a monatomic ideal gas.)

I have W = (3/2)nRT1(V1^(gamma-1) V2^(1-gamma) times -1)

I tried to set it up and I got 56.4 but the answer was 30.3. Can someone tell me what I did wrong and tell me how to properly calculate it? Thanks!

• College Physics -

v= 7 moles,
T₁=300 K
V₁=1000cm³= 10⁻³ m³
V₂=0.316•10⁻³ m³

W= {(vRT₁)/(γ-1)} •[1-(V₁/V₂)^(γ-1)]=
γ=(i+2)/I =(3+2)/3 = 5/3
γ-1=5/3 -1 =2/3= 0.667
W=- {(vRT₁)/(γ-1)} •[1-(V₁/V₂)^(γ-1)]=
= - { 7•8.31•300/0.667}•[1- (10⁻³/0.316•10⁻³)^0.667] =
= 30252 J =30.252 kJ ≈ 30.3 kJ

• College Physics -

An ice skater spinning with outstretched arms has an angular speed of 5.0$${\rm rad/s}$$ . She tucks in her arms, decreasing her moment of inertia by 19$${\rm \%}$$ .

By what factor does the skater's kinetic energy change? (Neglect any frictional effects.)

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