A perfect gas (0.1 mol) having = 1.50R (independent of temperature) undergoes the above transformation from point 1 to point 4. If each step is reversible, the total work done while going from point 1 to point 4 is (–) ___ J (nearest integer). [Given

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Solution

Q.

A perfect gas (0.1 mol) having $C_{v}$ = 1.50R (independent of temperature) undergoes the above transformation from point 1 to point 4. If each step is reversible, the total work done $(w)$ while going from point 1 to point 4 is (–) ___ J (nearest integer).

[Given : R = 0.082 L atm $K^{- 1}$ ${mol}^{- 1}$ ] [2025]

Ans.
(304)

$1 \to 2$ and $3 \to 4$ are isochoric processes. For isochoric processes $W (P Δ V) = 0$

$W_{2 \to 3} = - P (V_{3} - V_{2})$

$= - 3 atm (2 L - 1 L)$

$= - 3 atm L = - 3 \times 101.3 J = - 303.9 J$

$W_{1 \to 4} = W_{1 \to 2} + W_{2 \to 3} + W_{3 \to 4}$

$= 0 - 303.9 J + 0 = - 303.9 J = - 304 J$

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