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

Question

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]

Smart Achievers · Accepted Answer

(304)

$C_{v}$ and $3 \to 4$ are isochoric processes. For isochoric processes $W (P Δ V) = 0$

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

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

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

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

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

Solution

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Solution

Q. A perfect gas (0.1 mol) having Cv = 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-1mol-1] [2025]

Ans. (304) 1→2 and 3→4 are isochoric processes. For isochoric processes W(PΔV)=0 W2→3=-P(V3-V2) =-3 atm (2 L-1 L) =-3 atm L=-3×101.3 J=-303.9 J W1→4=W1→2+W2→3+W3→4 =0-303.9 J+0=-303.9 J=-304 J

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