Thermodynamics and Thermochemistry 1 Question 39

42. An ideal gas in thermally insulated vessel at internal pressure =p1, volume =V1 and absolute temperature =T1 expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are p2,V2 and T2, respectively. For this expansion

(a) q=0

(b) T2=T1

(c) p2V2=p1V1

(d) p2V2γ=p1V1γ

(2014 Adv.)

Show Answer

Solution:

  1. PLAN This problem includes concept of isothermal adiabatic irreversible expansion.

Process is adiabatic because of the use of thermal insolution therefore, q=0

pext =0

w=pextΔV=0×ΔV=0

Internal energy can be written as

ΔU=q+W=0

The change in internal energy of an ideal gas depends only on temperature and change in internal energy (ΔU)=0 therefore, ΔT=0 hence, process is isothermal and

and

T2=T1 p2V2=p1V1

(d) p2V2γ=p1V1γ is incorrect, it is valid for adiabatic reversible process.

Hence, only (a), (b) and (c) are correct choices.