What would be the SI unit for the quantity pV 2T 2/n ?

Exercises · 5.20

Q. What would be the SI unit for the quantity pV 2T 2/n ?

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Step 1 – SI unit of each quantity

p:\ \text{pascal (Pa)} = \text{kg m}^{-1}\text{s}^{-2}, \qquad V:\ \text{m}^3, \qquad T:\ \text{K}, \qquad n:\ \text{mol}

Step 2 – Raise $V$ and $T$ to the powers in the expression

V^2 \to (\text{m}^3)^2 = \text{m}^6, \qquad T^2 \to \text{K}^2

Step 3 – Assemble the full unit of $pV^2T^2/n$

\frac{pV^2T^2}{n} \to \frac{(\text{kg m}^{-1}\text{s}^{-2})(\text{m}^6)(\text{K}^2)}{\text{mol}}

Step 4 – Simplify the powers of metre …

Q.What would be the SI unit for the quantity pV 2T 2/n ?