The volume of a given weight of gas varies directly as its absolute temperature t and inversely as its pressure p. If the volume is 4.45 m^3 when p=225 kilo pascals (kpa) and t = 305 K, find the volumn when p = 325 kpa and t = 354 k.

use the relation

P1*V1/T1 = P2*V2/T2
and solve for V2. They tell you all the other numbers. You can use the units provided.
225*4.45/305 = 325*V2/354

To find the volume when p = 325 kPa and t = 354 K, we'll use the given relationship that the volume varies directly with the temperature and inversely with the pressure. Let's set up a proportion to solve for the volume.

First, let's write the direct variation equation for the volume and temperature:

Volume = k * Temperature

where k is the constant of variation.

Next, let's write the inverse variation equation for the volume and pressure:

Volume = k / Pressure

Combining these equations, we get:

Volume = k * Temperature / Pressure

Now, we can plug in the values from the first scenario to find the constant of variation, k:

4.45 m^3 = k * 305 K / 225 kPa

To solve for k, we can rearrange the equation:

k = 4.45 m^3 * 225 kPa / 305 K

k ≈ 3.272131147541 mi^3 * psi / °R

Now that we have the value of k, we can use it to find the volume in the second scenario:

Volume = k * Temperature / Pressure

Volume = 3.272131147541 mi^3 * psi / °R * 354 K / 325 kPa

Volume ≈ 3.563 mi^3 * psi / °R

Therefore, the volume when p = 325 kPa and t = 354 K is approximately 3.563 mi^3 * psi / °R.