Question

One mole of an ideal gas (group 18) at 27 ℃ and 1 atm expands adiabatically from a volume of 10 dm3 to 20 dm3. Calculate:
(i) q
(ii) w
(iii) ΔU
(iv) ΔH
(v) Final temperature of the gas.

Answer 1

T= 27°C= 27+273

P= 1atm

V₁= 10dm³

V₂= 20dm³

1. q= 0, for an adiabatic expansion, heat is neither gained nor lost by the system.

2. w= -P(V₂-V₁)

w= -1(20-10)

w= -10L.atm

1L.atm= 101.3J

-10L.atm= -10 x 101.3J= -1013J

3. ∆U = q+w

Since q= 0 (adiabatic)

∆U=w

∆U=-1013J

4. ∆H=∆U+P∆V

∆H=-1013+1(20-10)

∆H= -1013+10

∆H= -1003J

5. V₁= 10dm³ T₁= 300K

V₂= 20dm³ T₂= ?

V₁/T₁ = V₂/T₂

T₂= V₂T₁/V₁ = 20x300/10

= 600K = 327°C