2 mole of an ideal gas at 27 degree celcius and 1 atm pressure expand isothermally and reversibly till its pressure becomes 0.25 atm . calculate q , w and delta u

In a reversible isothermal expansion of a gas,at constant temperature,
       
T = 273 + 27 = 300K and n = 2

                                W=-2.303 nRT logp1p2     = -2.303 × 2 × 0.082 × 300 × log10.25      = -68.21J    

At constant temperature,
                 ΔU = 0         (First law of thermodyanamics, ΔU = q + W,and for irreversible process q=-W)
      and,
                W= -q = 68.21J
                                  

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∆U equals zero as for an ideal gas it is just a function of temperature and with no change in temperature, there's no change in it as well.

From above q=-w

Also W= -p∆v
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Also As T is constant, PV is constant.

Using relation work=-nrt ln(Pi/Pf)
=-68.3 l atm

now q=68.3 L atm
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