Question

A cylinder with a piston contains 0.200 mol of oxygen at 2.40×105 Pa and 340 K . The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure.

Find the work done by the gas during the initial expansion.

Answer 1

Work done by the gas during initial expansion is 564 J.

Step-by-step explanation:

Given :

Number of moles, n = 0.200

Initial pressure, P = 2.40 x 10⁵ Pa

Initial temperature, T = 340 K

According to the problem, it consider oxygen as an ideal gas. Hence, ideal gas equation can be applied on oxygen. Thus,

PV = nRT

Here P is pressure, V is volume, n is number of mole, R is universal gas constant and T is temperature.

V = (nRT)/P

Substitute the suitable values in the above equation.

`V = (0.2*8.31*340)/(2.40*10^(5) )`

V = 2.35 x 10⁻³ m³

It is the initial volume of the gas.

According to the problem, the gas expands isobarically i.e. its pressure remains same throughout the process.

But its volume changes to twice of initial volume i.e.

V₁ = 2V

Work done during isobaric process is given by the equation :

W = P ( V₁ - V )

Substitute the suitable values in the above equation.

W = 2.40 x 10⁵ x ( 2 x 2.35 x 10⁻³ - 2.35 x 10⁻³ )

W = 564 J