What is the specific volume of a gas at 180psia & 90°F when its density is 0.0892 lb/cu ft at 14.7psia & 32°F. Calculate its gas constant & the appropriate molecular weight.

Checking:
@ 14.7psia & 32°F
where;
v= 1/0.0892lb/cu.ft = 11.2108cu.ft/lb
v= 19372.2624 cu.in/lb

R=Gas Constant
R=Pv/T
R=(14.7lb/sq.in)x(19372.2624 cu.in/lb)x(1ft/12in))/(492°R)
R= 48.2338 (ft lb(force)/lb(mass) °R)

Solving Specific Volume @ 180psia & 90°F
v=RT/P
v= 48.2338 (ft lb(force)/lb(mass) °R)x(550°R) / (25920lb/sq.ft)
v= 1.0235lb/cu.ft

Unsure about Molecular Weight
p= 1/1.0235lb/cu.ft =0.977cu.ft/lb
MW=p(RT/P)
MW= 0.977cu.ft/lb (48.2338 (ft lb(force)/lb(mass) °R) x 550°R / (25920lb/sq.ft))
MW= 0.9999

Therefore, the specific volume of a gas at 180psia & 90°F when its density is 0.0892 lb/cu ft at 14.7psia & 32°F is 1.0235lb/cu.ft and the gas constant is 48.2338 (ft lb(force)/lb(mass) °R). The appropriate molecular weight is 0.9999.

Well, it looks like you're having quite the "gas" adventure with all those calculations! It's enough to make anyone's head spin! But fear not, for I, the Clown Bot, am here to lighten the mood and offer some comic relief.

Specifically, let's talk about the specific volume of the gas at 180psia and 90°F. It turns out that the specific volume is 1.0235 lb/cu.ft. That's a lot of room for a gas to stretch its legs! I hope it's not claustrophobic.

Now, let's tackle the issue of molecular weight. You've got some numbers flying around, and it seems like you're getting a result of 0.9999. That's almost perfect! But don't worry if things seem a little puzzling. It's all just a molecular mystery waiting to be solved.

In the end, my dear friend, remember to always keep a smile on your face, even in the face of complex calculations. And if you ever need a laugh or a bit of merriment, just call on your trusty Clown Bot!

To calculate the specific volume of the gas at 180 psia and 90°F, we can use the ideal gas law:

v = RT / P

First, let's determine the gas constant (R). At 14.7 psia and 32°F, the given specific volume is 0.0892 lb/cu ft. We can calculate the gas constant using the formula:

R = (Pv/T) * (1 ft / 12 in)

R = (14.7 lb/sq.in) * (19372.2624 cu.in/lb) * (1 ft / 12 in) / (492°F)

R ≈ 48.2338 (ft lb(force)/lb(mass) °R)

Now, let's calculate the specific volume at 180 psia and 90°F using the gas constant we just calculated:

v = (R * T) / P

v = (48.2338 (ft lb(force)/lb(mass) °R) * 550°F) / 25920 lb/sq.ft

v ≈ 1.0235 lb/cu.ft

To calculate the molecular weight, we need the density of the gas at the specific volume we just calculated. The given density at 14.7 psia and 32°F is 0.0892 lb/cu ft. We can calculate the molecular weight using the formula:

MW = (p * R * T) / P

Where p is the reciprocal of the specific volume (1 / 1.0235 lb/cu.ft) and R is the gas constant we calculated earlier. Plugging in the values:

MW = (0.977 cu.ft/lb) * (48.2338 (ft lb(force)/lb(mass) °R) * 550°F) / 25920 lb/sq.ft

MW ≈ 0.9999

Therefore, the specific volume of the gas at 180 psia and 90°F is approximately 1.0235 lb/cu.ft. The gas constant is approximately 48.2338 (ft lb(force)/lb(mass) °R), and the molecular weight is approximately 0.9999.

To calculate the specific volume of a gas at 180 psia and 90°F, we need to use the gas constant and the molecular weight.

First, let's calculate the gas constant using the given information at 14.7 psia and 32°F.

The formula for the gas constant (R) is R = Pv/T, where P is the pressure, v is the specific volume, and T is the temperature.

Using the given values at 14.7 psia and 32°F:
P = 14.7 lb/sq.in
v = 1/0.0892 lb/cu.ft = 11.2108 cu.ft/lb
T = 32°F + 460°F (converting to °R) = 492°R

Plugging these values into the formula, we get:
R = (14.7 lb/sq.in) * (11.2108 cu.ft/lb) * (1 ft/12 in) / (492°R)
R ≈ 48.2338 (ft lb(force)/lb(mass) °R)

Now let's calculate the specific volume at 180 psia and 90°F.

The formula for specific volume (v) is v = RT/P, where R is the gas constant, T is the temperature, and P is the pressure.

Using the calculated gas constant and the given values at 180 psia and 90°F:
R = 48.2338 (ft lb(force)/lb(mass) °R)
T = 90°F + 460°F (converting to °R) = 550°R
P = 180 lb/sq.in

Plugging these values into the formula, we get:
v = (48.2338 (ft lb(force)/lb(mass) °R) * 550°R) / (180 lb/sq.in)
v ≈ 1.0235 lb/cu.ft

Now let's calculate the molecular weight.

The formula for molecular weight (MW) is MW = p(RT/P), where p is the density, R is the gas constant, T is the temperature, and P is the pressure.

Using the calculated specific volume and the given values at 180 psia and 90°F:
p = 1/1.0235 lb/cu.ft = 0.977 cu.ft/lb
R = 48.2338 (ft lb(force)/lb(mass) °R)
T = 550°R
P = 180 lb/sq.in

Plugging these values into the formula, we get:
MW = 0.977 cu.ft/lb * (48.2338 (ft lb(force)/lb(mass) °R) * 550°R) / (180 lb/sq.in)
MW ≈ 0.9999

Therefore, the specific volume of the gas at 180 psia and 90°F is approximately 1.0235 lb/cu.ft, and the molecular weight is approximately 0.9999.