The volume of a gas varies directly with its temperature and inversely with the pressure. If the volume of a certain gas is
20 cubic feet at a temperature of
350K and a pressure of 35
pounds per square inch, what is the volume of the same gas at 330
K when the pressure is 30
pounds per square inch?
V = kt/p
for the given data:
20 = k(350)/35
k = 20(35)/350 = 2
V = 2t/p
when t=330, p=30
V = 2(330)/30 = 22
PV=kT, so PV/T=k is constant. o, you need V such that
30V/330 = 35*20/350
V/11 = 2
V = 22
Well, it seems like this gas is quite picky when it comes to its volume, temperature, and pressure. Let's solve this riddle!
We know that the volume of the gas varies directly with its temperature and inversely with the pressure. So, we can use the formula:
V1/T1 * P1 = V2/T2 * P2
Now, let's plug in the given values:
V1 = 20 cubic feet
T1 = 350K
P1 = 35 pounds per square inch
T2 = 330K
P2 = 30 pounds per square inch
Using the formula, we get:
20/350 * 35 = V2/330 * 30
Simplifying the equation, we have:
V2/330 = (20/350) * (30/35)
Now, let's calculate:
V2/330 = (2/7) * (6/7)
V2/330 = 12/49
To solve for V2, we can cross multiply:
V2 = (12/49) * 330
Hence, the volume of the gas at 330K and a pressure of 30 pounds per square inch is approximately 80 cubic feet.
So, out with the math and in with the giggles - the volume of the gas is 80 cubic feet. Enjoy the spaciousness!
To solve this problem, we're given that the volume of a gas varies directly with its temperature and inversely with its pressure. We need to find the volume of the gas at a different temperature and pressure.
Let's assign variables to the values given:
V1 = initial volume = 20 cubic feet
T1 = initial temperature = 350 K
P1 = initial pressure = 35 pounds per square inch
T2 = new temperature = 330 K
P2 = new pressure = 30 pounds per square inch
Using the given information, we can set up the following equation:
V1 / T1 * P1 = V2 / T2 * P2
Plugging in the values we know:
20 / 350 * 35 = V2 / 330 * 30
Simplifying the equation:
7000 / 350 = V2 / 9900
Simplifying further:
20 = V2 / 9900
To solve for V2, we can cross multiply:
20 * 9900 = V2
V2 = 198,000 cubic feet
Therefore, the volume of the gas at a temperature of 330 K and a pressure of 30 pounds per square inch would be 198,000 cubic feet.
To solve this problem, we can use the combined variation formula and plug in the given values.
The combined variation formula for direct and inverse variation is:
V1 / V2 = (T1 / T2) * (P2 / P1)
Let's break down the formula:
V1 and V2 represent the volumes at two different temperatures and pressures.
T1 and T2 represent the temperatures at which the volumes are measured.
P1 and P2 represent the pressures at which the volumes are measured.
Now let's substitute the given values into the formula:
V1 = 20 cubic feet
T1 = 350 K
P1 = 35 pounds per square inch
V2 is what we're trying to find.
T2 = 330 K
P2 = 30 pounds per square inch
Now let's plug in the known values into the formula and solve for V2:
20 / V2 = (350 / 330) * (30 / 35)
First, we simplify the values within the parentheses:
20 / V2 = (1.0606) * (0.8571)
Then we multiply the two values within the parentheses:
20 / V2 = 0.9090
To solve for V2, we rearrange the equation:
V2 = 20 / 0.9090
Now we can calculate V2:
V2 ≈ 22.0002 cubic feet
Therefore, the volume of the same gas at 330 K and a pressure of 30 pounds per square inch is approximately 22.0002 cubic feet.