Stephen Hawking’s seminal paper on black hole radiation, often referred to as **Hawking Radiation**, explains how black holes, previously thought to only absorb matter and energy, can actually emit radiation and eventually lose all their energy. This discovery has profound implications for black hole thermodynamics and the fate of black holes.

### 1. **Quantum Field Theory Near the Event Horizon**
Hawking’s explanation starts with quantum mechanics and general relativity. Near the event horizon of a black hole, quantum field theory predicts that particle-antiparticle pairs are constantly being created from the vacuum due to the uncertainty principle. Normally, these pairs would quickly annihilate each other. However, at the event horizon, one of these particles can fall into the black hole while the other escapes.

### 2. **Particle Escape Mechanism**
In the context of the event horizon, one of the particles of the pair can escape into space, while the other falls into the black hole. To an outside observer, it appears as if the black hole is radiating particles. This escaping particle carries positive energy, while the particle that falls into the black hole has negative energy relative to the outside observer.

### 3. **Energy Loss and Radiation**
Since the escaping particle carries energy away from the black hole, the black hole must lose an equivalent amount of energy. Over time, this energy loss causes the black hole to shrink. As the black hole emits more radiation, it loses more mass and energy, gradually getting smaller.

The radiation emitted by the black hole is thermal in nature, resembling blackbody radiation, with a temperature inversely proportional to the mass of the black hole. Smaller black holes emit more radiation and therefore lose mass more rapidly, leading to an acceleration of the radiation process as the black hole shrinks.

### 4. **Black Hole Evaporation**
As the black hole continues to radiate energy, its mass decreases. This process, known as **black hole evaporation**, predicts that over a very long period, a black hole will radiate away all its energy. The temperature of the radiation increases as the black hole gets smaller, and the rate of radiation increases exponentially as the black hole approaches its final moments.

Eventually, when the black hole becomes sufficiently small, it will radiate away the last of its mass and disappear entirely. This leads to the conclusion that black holes are not eternal but will eventually radiate away all their energy and vanish.

### 5. **Implications for Thermodynamics**
Hawking’s discovery revolutionized the understanding of black hole thermodynamics. It shows that black holes must obey the laws of thermodynamics, particularly the second law, where entropy (disorder) must increase over time. The radiation emitted by the black hole carries entropy, ensuring that the total entropy of the universe increases even as the black hole loses mass and energy.

### Conclusion
A black hole must eventually radiate away all its energy because the quantum mechanical effects near its event horizon allow particles to escape, leading to a gradual loss of mass and energy through Hawking Radiation. Over immense periods, this process will cause the black hole to shrink and eventually disappear.