A monatomic idea gas with an initial pressure of 500 kPa and an initial volume o

Question

A monatomic idea gas with an initial pressure of 500 kPa and an initial volume of 1.80 L expands isothermally to a final volume of 5.20 L. How much work is done on the gas in this process? (PLEASE SHOW ALL WORK, NO WORK NO CREDIT)

A. 1700 J

B. 875 J

C. 1570 J

D. 900 J

E. 955 J

(PLEASE SHOW ALL WORK, NO WORK NO CREDIT)

Explanation / Answer

ideal gas --> pV=nRT Now from the ideal gas equation we can work out the number of moles n in terms of T n=pV/RT=(500*10^3*0.0018)/(8.31)T = 108.3 (1/T) work done = integrate p dV= nRT/V dV = nRT ln (V_f/V_i) (note that we can take the T out of the integral because it is a constant in isothermal expansion) Hence work done = nRT ln (V_f/V_i)= 108.3*8.31*ln( 5.2/1.8)=954.7 J which is option E.

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