Discussion Forum

One mole of monoatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100K and the universal gas constant  R= 8.0 j mol^-1 K^-1 , the decrease in its internal energy in joule, is ..............

Answer:

Explanation:

n=1,  $r=\frac{5}{3}$

T-V equation in adiabatic process is

TV^r-1 = constant

T₁ V₁^r-1   =T₂ V₂^r-1

$\Rightarrow$ T₂ = T₁  $(\frac{V_{1}}{V_{2}})^{r-1}$   = $100\times (\frac{1}{8})^{\frac{2}{3}}$

$\Rightarrow$     T₂ =25 K

$C_{v}=\frac{3}{2}R $ for monoactomic gas

$\therefore$   $\triangle U = n C_{v}\triangle T= n\times (\frac{3R}{2}) (T_{2}-T_{1})$

=  $1 \times \frac{3}{2}\times 8 \times (25-100)$

=  -900 J

Therefore, Decreases in internal energy = 900 J