Answer to Question #172778 in Molecular Physics | Thermodynamics for Bahaa

Question

An ideal gas undergoes the following reversible cycle: (i) an iso￾baric expansion from the state (P1,V1) to the state (P1,V2); (ii) an 
isochoric reduction in pressure to the state (P2,V2); (iii) an isobaric 
reduction in volume to the state (P2,V1); (iv) an isochoric increase 
in pressure back to the original state (P1,V1). (a) What work is done 
on the gas in this cycle? (b) If P1 = 3.0 atm, P2 = 1.0 atm, V1 = 1.0 L 
and V2 = 2.0 L, how much work is done on the gas in traversing the 

• cycle 100 times?

Answer 1

(a) Work = area of rectangle ABCD

$= (P_1-P_2)(V_2-V_1)$

(b) Work = 100 \times area of rectangle ABCD

$= 100 \times 2 \; atm \times 1 \;l\\ = 100 \times 2 \times 1.013 \times 10^5 \;Pa \times 10^{-3} \;m^3\\ = 2.026 \times 10^4 \;J$