ThermodynamicsHard
Question
The equation of state for one mole of a gas is PV = RT + BP, where B is a constant, independent of temperature. The internal energy of fixed amount of gas is the function of temperature only. If one mole of the above gas is isothermally expanded from 12 L to 22 L at a constant external pressure of 1 bar at 400 K, then the change in enthalpy of the gas is approximately (B = 2 L/mol)
Options
A.0
B.−3.32 J
C.−332 J
D.−166 J
Solution
$\Delta U = 0$
$\Delta H = \Delta U + \Delta(PV) = 0 + B\left( P_{2} - P_{1} \right) = B.\frac{RT}{V_{2} - B} - \frac{RT}{V_{1} - B}$
$= 2 \times 8.314 \times 400\left( \frac{1}{22 - 2} - \frac{1}{12 - 2} \right) = - 332.56\text{ J}$
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