Volume of a gas at 27degree centigrade and 760mm pressure is 200cm cube then find the volume of same gas at -3degree centigrade and 760mm pressure
Use the ideal gas equation:
PV = nRT
=> PV/T = nR
The amount of substance 'n' and the universal gas constant 'R' is the same in this case, hence, PV/T will remain constant:
=> (PV/T)1 = (PV/T)2
(Note that temperature must be taken in Kelvin)
=> (760*200)/(300) = (760*V2)/(270)
=> V2 = 270*(2/3)
= 180
Since the answer is obtained in the same units as V1, the volume is 180 cm cube
To find the volume of the gas at a different temperature, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
In this case, the pressure (P) and the number of moles (n) are constant, so we can rewrite the equation as:
V₁/T₁ = V₂/T₂
Let's plug the given values into the equation:
V₁ = 200 cm³
T₁ = 27 °C (convert to Kelvin: 27 + 273 = 300 K)
T₂ = -3 °C (convert to Kelvin: -3 + 273 = 270 K)
Now, rearrange the equation to solve for V₂:
V₂ = (V₁ * T₂) / T₁
Substituting the values:
V₂ = (200 cm³ * 270 K) / 300 K
V₂ = 180 cm³
Therefore, the volume of the same gas at -3 degrees Celsius and 760 mm pressure is 180 cm³.