Solve the problem.
The pressure of a gas varies jointly as the amount of the gas (measured in moles) and the temperature and inversely as the volume of the gas. If the pressure is 1170 (kiloPascals) when the number of moles is 6, the temperature is 260 kelvin , and the volume is 720cc , find the pressure when the number of moles is 3, the temperature is 280k , and the volume is180 cc .
To solve the problem, we can use the formula for joint and inverse variation. The formula is given as:
P = k * (n * T) / V
Where:
P is the pressure of the gas
n is the number of moles of the gas
T is the temperature of the gas
V is the volume of the gas
k is the constant of variation
We need to find the value of k using the given information about pressure, number of moles, temperature, and volume.
Since the pressure is 1170 kPa when the number of moles is 6, the temperature is 260 K, and the volume is 720 cc, we can substitute these values into the formula to solve for k:
1170 = k * (6 * 260) / 720
1170 = k * 1560 / 720
1170 = k * 13 / 6
k = (1170 * 6) / 13
k = 540
Now that we have the value of k, we can substitute it into the formula to find the pressure when the number of moles is 3, the temperature is 280 K, and the volume is 180 cc:
P = 540 * (3 * 280) / 180
P = 8100 / 180
P = 45 kPa
Therefore, the pressure when the number of moles is 3, the temperature is 280 K, and the volume is 180 cc is 45 kPa.
To solve this problem, we can use the formula for joint and inverse variation:
Pressure = (k * Amount of gas * Temperature) / Volume
where k is the constant of variation.
Given information:
Pressure = 1170 kPa
Number of moles = 6
Temperature = 260 K
Volume = 720 cc
To find the constant of variation, we can rearrange the formula:
k = (Pressure * Volume) / (Amount of gas * Temperature)
Substituting the given values:
k = (1170 * 720) / (6 * 260)
k ≈ 100
Now, we can use this value of k to find the pressure when the number of moles is 3, the temperature is 280 K, and the volume is 180 cc:
Pressure = (k * Amount of gas * Temperature) / Volume
Pressure = (100 * 3 * 280) / 180
Pressure ≈ 466.67 kPa
Therefore, the pressure when the number of moles is 3, the temperature is 280 K, and the volume is 180 cc is approximately 466.67 kPa.
P = kmT/V
(usually written as PV = knRT)
Anyway, that means that
PV/Tm = k a constant
So, you want P such that
180P/(3*280) = (1170*720)/(6*260)