Match List-I with List-II.
| List-I | List-II |
| (A) Heat capacity of body | (I) \( J\,kg^{-1} \) |
| (B) Specific heat capacity of body | (II) \( J\,K^{-1} \) |
| (C) Latent heat | (III) \( J\,kg^{-1}K^{-1} \) |
| (D) Thermal conductivity | (IV) \( J\,m^{-1}K^{-1}s^{-1} \) |
In the given cycle ABCDA, the heat required for an ideal monoatomic gas will be:

The given circuit works as: 
Let the lines $L_1 : \vec r = \hat i + 2\hat j + 3\hat k + \lambda(2\hat i + 3\hat j + 4\hat k)$, $\lambda \in \mathbb{R}$ and $L_2 : \vec r = (4\hat i + \hat j) + \mu(5\hat i + + 2\hat j + \hat k)$, $\mu \in \mathbb{R}$ intersect at the point $R$. Let $P$ and $Q$ be the points lying on lines $L_1$ and $L_2$, respectively, such that $|PR|=\sqrt{29}$ and $|PQ|=\sqrt{\frac{47}{3}}$. If the point $P$ lies in the first octant, then $27(QR)^2$ is equal to}