2 mole of ideal monoatomic gas is expanded from initial pressure of 5 atm and initial temperature of 300 K to final pressure of 4 atm against constant external pressure of 2 atm adiabatically. What is

Question

2 mole of ideal monoatomic gas is expanded from initial pressure of 5 atm and initial temperature of 300 K to final pressure of 4 atm against constant external pressure of 2 atm adiabatically. What is the Δ H of the process. Take R = 2 cal mo l − 1 K − 1 .

TestHub · Accepted Answer

Question Explanation: Finding enthalpy change for adiabatic expansion of an ideal gas. Concept: First Law of Thermodynamics, adiabatic irreversible process.

Solution: In an adiabatic process, $q = 0$ , so $Δ U = W$ . For a monoatomic gas,

$C_{V} = \frac{3}{2} R$ and $C_{p} = \frac{5}{2} R$ . We find the final temperature $T_{2}$ first.

Let $T_{f}$ be the final temperature.

$W = Δ U \Rightarrow - P_{e x t} (V_{f} - V_{i}) = n C_{V} (T_{f} - T_{i})$

$- 2 [\frac{2 R T _{f}}{4} - \frac{2 R ( 300 )}{5}] = 2 \times \frac{3}{2} R (T_{f} - 300)$

$T_{f} = 285 K$

$Δ H = n C_{p} (T_{2} - T_{1}) = 2 \times \frac{5}{2} R (285 - 300) = 5 R (- 15) = - 75 R c a l$

Assuming $R \approx 2 c a l / m o l . K$ , then $Δ H = - 75 \times 2 = - 150 c a l$ .

Final Answer: Option (A)

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