Question

2 kilograms of ideal gas air undergoes an isothermal expansion from 3MPa and 300K to 1Mpa. Determine the work done, the change in specific internal energy, and the heat transferred.

Answer 1

N moles of air in 2kg mass

21% O2 and 78% N2. (The 1% noble gases will be of no consequence here).
O2 mol.mass = 32g/mol x 0.21 = 6.72 moles.
N2 mol.mass = 28g/mol. x 0.78 = 21.84 moles.
Total = 28.56 g/mol.

no of moles in 2000grams of air = 2000/28.56 = 70.02 moles

N= m / mass per mole

- NRTln(p1/p2) = 70.2(8.314) * 300 ln(3) = -192.36 Kj

P1 = NRT/ V1

V1 = NRT/ P1

V2 = NRT/P2

By convention, work is defined as the work the system does on its environment. If, for example, the system expands by a piston moving in the direction of force applied by the internal pressure of a gas, then the work is counted as negative, and as this work is done by using internal energy of the system, the result is that the internal energy decreases. Conversely, if the environment does work on the system so that its internal energy increases, the work is counted as positive.

In an Isothermal process the temperature is constant. Hence, the internal energy is constant, and the net change in internal energy is ZERO

t

heat transfered Q = W