An ideal gas is expanded isothermally so that its volume changes by a factor of 1.4, and the pressure

An ideal gas is expanded isothermally so that its volume changes by a factor of 1.4, and the pressure by delta p = 80 kPa. Find the starting gas pressure.

We start with a brief notation given and the conversion of units to the SI system.

Given:

T – const;

V1;

V2 = V1 / 1.4;

Δp = 200 kPa = 200 * 10 ^ 3 Pa.

Find: p1 -?

The given process is isothermal. Let’s apply the Boyle-Mariotte law to it:

p1 * V1 = p2 * V2.

As the gas was compressed, the pressure increased:

p2 = (p1 + Δp);

We get equality:

p1 * V1 = (p1 + Δp) * V1 / 1.4;

p1 = (p1 + Δp) / 1.4;

1.4 * p1 = p1 + Δp;

0.4 * p1 = Δp;

p1 = Δp / 0.4.

It remains to substitute the values and calculate:

p1 = 200 * 10³ / 0.4 = 500,000 Pa = 5 * 10 ^ 5 Pa