What is a carnot refrigerator ? Find the relation between the coefficient of performance$\left(\eta \text{'}\right)$ of a carnot refrigerator and the efficiency of a carnot heat engine$\left(\eta \right)$.

A moving lead bullet at $27°\mathrm{C}$ Struck against an obstacle. Assuming that 25% of its heat is absorbed by the obstacle, what was the velocity of the bullet ? (Melting point of lead $={327}^{o}C$, Specific heat of lead $=0.03 cal/gm o^{}C$

Latent heat of fusion of lead$=6 cal/gm and J=4.2 Joule/cal$).

An ideal gas is filled in closed rigid and thermally insulated container. A  coil of $100\Omega$ resistor carrying current A for $5$ minutes supplies heat to the gas. The change in internal energy of the gas is