Question

A certain gas is expanded from (1 L, 10 atm) to (4 L, 5 atm) against a constant external pressure of 1 atm. If the initial temperature of the gas is 300 K and the heat capacity for the process is $50J/C^0$, the enthalpy change during the process is :

• A. 15 kJ
• B. 15.7 kJ
• C. 14.3 kJ
• D. 14.7 kJ

Answer 1

The correct option is B 15.7 kJ

The amount of gas expanded using the ideal gas equation:
$P_1{V}_1=nR{T}_1$
$10\times 1=n\times 0.0821\times 300$
n = 0.4 mole
Final temperature obtained:
$P_2{V}_2=nR{T}_2$
$5\times 4=0.4\times 0.0821\times T_2$
$T_2$ = 600 K
Work done during expansion = $-P_{ext}(V_2-V_1$)
= -1(4-1) atm L = 300 J
and heat involved = $Q=C_{p}dT$
= $50\times (600-300$) = 15000 J
Using equation $\delta U=\delta Q+\delta W$
= 15000-300 = 14700 J
and $\delta H=\delta U+\delta \left(PV\right)$
= 14700 + $(4\times 5-10\times 1)\times 100$ J
=15700J = 15.7 kJ