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Q.

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 $50 J /^{\circ} C$ . Then the enthalpy change during the process is : ( 1 L atm = 100 J)

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a

$Δ H = 15 kJ$

b

$Δ H = 15.7 kJ$

c

$Δ H = 14.4 kJ$

d

$Δ H = 14.7 kJ$

answer is B.

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Detailed Solution

The pressure volume diagram for this problem is given below;

Question Image

$\begin{array}{l} w = - 1 \times 3 L - atm = - 300 J \\ \begin{aligned} \frac{10 \times 1}{300} & = \frac{5 \times 4}{T} \Rightarrow T = 600 K \\ q & = 50 \times 300 = 15000 J \\ \Rightarrow Δ U & = q + w = 14700 J \\ Δ H & = Δ U + Δ (P V) \\ = 14700 + (20 - 10) \times 100 = 15700 J \end{aligned} \end{array}$

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