57. Consider a Carnot heat engine operating between a heat reservoir at temperature 600 K , and an external atmosphere at temperature 300 K . In one cycle, 1000 kJ of heat is extracted from the heat reservoir, and the associated work is input to a reversible refrigerator that operates between 200 K and the same external atmosphere at 300 K . The refrigerator completes one cycle and releases heat into the atmosphere. How much heat is released into the atmosphere at the end of one cycle of the combined system?

Two spherical bodies A and B each of mass $M$ and radius $R$ are located such that their centers are apart by a distance of $4 R$ as shown in the figure. An object $C$ of mass $m$ is thrown from the surface of A directly towards the center of B with a speed $v_0=2 v_{\text {min }}$, where $v_m$ in is the minimum speed needed for $C$ to reach the surface of $B$. Given that $G$ is the universal gravitational constant, how does the speed $v(x)$ of C change as a function of its distance from the center of A?

Consider the Bohr model of an atom where an electron of charge $-e$ revolves around a nucleus of charge $+e$ in an orbit of radius $r$. The electron has an orbital angular momentum $2 h$. If the nucleus had charge $+2 e$, what would have been the radius of the orbit of the electron with the same principal quantum number?

A quantity has been measured to have a value of 0.00230 in some units. How many significant figures does the measured value have?