Question

One mole of an ideal gas $\left( C_{v,m} = \frac{5}{2}R \right)$at 300 K and 5 atm is expanded adiabatically to a final pressure of 2 atm against a constant pressure of 2 atm. Final temperature of the gas is :

• A. 270 K
• B. 273 K
• C. 248.5 K
• D. 200 K

Answer 1

Answer: (C)

248.5 K

Answer 2

q = 0

$\therefore\Delta$U = w

̃ nCv,m (T`2 – T1) = – Pext $\left\lbrack \frac{nRT_{2}}{P_{2}} - \frac{nRT_{1}}{P_{1}} \right\rbrack$

$\therefore$ Cv, m [T2 – T1] = Pext . $R\left\lbrack \frac{T_{1}}{P_{1}} - \frac{T_{2}}{T_{2}} \right\rbrack \Rightarrow \frac{5}{2}$

R [T2 – 300] = 2 × R$\left\lbrack \frac{300}{5} - \frac{T_{2}}{2} \right\rbrack$̃ T2 = 248.5 K