A

Step 1: Given the equation for volume: $V = k T^{\frac{2}{3}}$, where $k$ is a constant. \n Step 2: When the temperature changes, the work done, $W$, can be calculated using the relationship between volume and temperature. \n Step 3: The change in work done for a monatomic gas can be described using the formula for the work done as the volume changes with temperature. Specifically, $W = k \Delta( T^{\frac{2}{3}})$. \n Step 4: By substituting in the given change in temperature $\Delta T = 90K$, we find the relationship relating $W$ to the universal gas constant $R$. \n Therefore, the value of $x = R$.