Question

One mole of monoatomic gas at tk is expanded from 1 l to 2 l adiabatically under a constant external pressure of 1 atm. The final temperature of

Answer 1

Answer:

final temperature is

Tf =  T- (2/ 3 R)

or Tf =  T- (2/ 3 X 0.0821)

Explanation:

Given

Initial volume V₁ = 1 L

Final volume V₂ = 2 L

Change in volume ΔV = 1 L

Adiabatic condition therefore, q = 0

Pressure P = 1 atm

no. of moles = 1 mol

final temperature Tf = ??

Solution

According to 1st law of thermodynamics

ΔU = w + q                      as q = 0

ΔU = w...........................(i)

also w = - P ΔV

by putting values

w = -1 atm. L

also Cv = R/ γ - 1

and γ = 5/3 (monoatomic gas)

R = 0.0821

Cv = 3/2 R  

Let the final temperature is Tf

and change in temperature

ΔT = Tf -T

n= 1

Also

ΔU = n Cv ΔT................(ii)

from equation i

w = 3/2 R (Tf -T)

(Tf -T) = -1/ (3/2 R)

Tf =  T- (2/ 3 R)

Tf =  T- (2/ 3 X 0.0821)