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

Δ H = 15

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Δ H = 15.7

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Δ H = 14.4

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Δ H = 14.7

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Solution

The correct option is A $Δ H = 15$ kJ
Let us consider the problem:
Given that
$C p = 50 j /^{0} c$
$p_{1} = 10 a t m a n d p_{2} = 5 a t m$
$v_{1} = 1 L a n d v_{2} = 4 L$
$T_{1} = 300 k$
$T_{2} = \frac{P_{2} V_{2} T_{2}}{P_{1} V_{1}}$
$= \frac{5 \times 4 \times 300}{10 \times 1} = 600 k$
Hence,
Entholpy change $Δ H = C p d t$
Implies that
$= 50 \times (600 - 300)$
$= 15000 J$
$= 15 k J$

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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)