Question

One mole of an ideal monoatomic gas at temperature $T$ and volume $1L$ expands to $2L$ against a constant external pressure of one atm under adiabatic conditions, then the final temperature of the gas will be :

• A. $T+\frac{2}{3\times 0.0821}$
• B. $T-\frac{2}{3\times 0.0821}$
• C. $\frac{T}{2^{5/3-1}}$
• D. $\frac{T}{2^{5/3+1}}$

Answer 1

The correct option is B $T-\frac{2}{3\times 0.0821}$

The case of irreversible adiabatic process.
$w=-P(V_f-V_i)$
${nC}_v(T_2-T_1)=-P(V_f-V_i)n=1$
$C_v=\frac{3}{2}R{T}_1=T$
$T_2=\frac{-P(V_f-V_i)}{{nC}_v}+T=T-\frac{\left(1atm\right)(2L-1L)}{\frac{3}{2}R}$
$T_2=T-\frac{2\left(Latm\right)}{3\times 0.0821\left(Latm{K}^{-1}{mole}^{-1}\right)}$