Answer:
The value of R is, 8.31
Step-by-step explanation:
Given the universal gas law:
pV = nRT ....[1]
where,
p = pressure
V = volume
T = temperature (Kelvin)
n = number of moles (quantity of gas particles)
R = universal gas constant
It is given that at a constant temperature of 1 K, the pressure and volume of 1 mole of gas vary inversely.
⇒T = 1 K and n = 1
Since, pressure and volume varies inversely.
⇒[tex]pV = k[/tex] where, k is constant
to find k:
From the given table:
p=2 and V = 4.155
then;
[tex]2 \cdot 4.155 = k[/tex]
⇒[tex]8.31 = k[/tex]
or
k = 8.31
[tex]pV =8.31[/tex]
We have to find value of R:
Substitute pV = 8.31 and the given values in [1] we have;
[tex]8.31 = 1 \cdot R \cdot 1[/tex]
⇒[tex]8.31 = R[/tex]
or
[tex]R = 8.31[/tex]
Therefore, the value of R is, 8.31
