Question

How to solve it.

(a) One mol of helium gas (considered ideal undergoes reversible isothermal
expansion from 20 dm3 to 70 dm3 at 298K Compute delta U, w and q

(b) If the gas in part (a) undergoes irreversible into vacuum, compute delta U, w, and q

(c) Show that for helium gas use in part (a) and (b)

(dU/dV)P = CvP/R

(d) Calculate delta u from
the relation in
part (C)​

Answer 1

Solution:-

Work done in an isothermal reversible process is given by-

W=−nRTln

V

1

V

2

Where,

n = no. of moles =1

R= molar gas constant =8.314Jmol

−1

K

−1

T= temperature =300K

V

1

=10dm

3

V

2

=20dm

3

∴W=−1×8.314×300×ln

10

20

⇒W=−2494.2×(ln2−ln1)=−1728.8 J=−1.73 kJ

Now, from first law of thermodynamics,

ΔU=ΔH+W

Since temperature is constant, i.e. ΔU=0.

∴ΔH=−W=−(−1.73)=+1.73KJ

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