A certain mass of gas is expanded from $(1 L, 10 a t m)$ to $(4 L, 5 a t m)$ against a constant external pressure of $1 a t m$ . If the initial temperature of the gas is $300 K$ and the heat capacity of the process is $50 J /^{\circ} C$ . Then the enthalpy change during the process is: $(1 L a t m ≃ 100 J)$ .

△ H = 15 k J

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△ H = 15.7 k J

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△ H = 14.4 k J

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△ H = 14.7 k J

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Solution

The correct option is D $△ H = 15.7 k J$
For the state 1
$P V = n R T$
$1 \times 10 = n (0.0821) (300)$
$n = 0.4$
For the state 2
$P V = n R T$
$4 \times 5 = 0.4 \times (0.0821) (T_{2})$
$T_{2} = 600 K$
$Δ U = q + W$
$= 50 (Δ T) + (- P_{e x}) (Δ V)$
$= 50 (600 - 300) - (1) (4 - 1)$
$= 15000 - 300$
$= 14700 J$
$Δ H = Δ U + Δ (P V)$
$= 14700 + (5 \times 4 - 10)$
$= 15700 J$
$= 15.7 k J$

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Similar questions

A certain mass of gas is expanded from (1L, 10 atm) to (4L, 5 atm) against a constant external pressure of 1 atm. If initial temperature of gas is 300K and the heat capacity of process is $50 J /^{\circ} C$ . Then the enthalpy change during the process is:
(1L atm = 100 J)