(Part marks) 1. Inertial confinement fusion, which is being considered as a source of power, can be approximated by a ra

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Part Marks 1 Inertial Confinement Fusion Which Is Being Considered As A Source Of Power Can Be Approximated By A Ra 1 (47.62 KiB) Viewed 52 times

Part Marks 1 Inertial Confinement Fusion Which Is Being Considered As A Source Of Power Can Be Approximated By A Ra 2 (71.04 KiB) Viewed 52 times

(Part marks) 1. Inertial confinement fusion, which is being considered as a source of power, can be approximated by a rapid adiabatic compression that reaches the high temperatures and densities required for fusion of hydrogen isotopes. [2] 141 (a) Show that the ratio of the volume before and after an adiabatic compression is given by () where is the final temperature, T, is the initial temperature and y is the heat capacity ratio. Assume that the gas being compressed is ideal (b) Using the result above, or otherwise, show that the ratio of the number density (number of particles per unit volume) betore, Mon, and after, men is given by :-(1) (c) Circulate the fusion reaction rate per unit volume given by R-10-ra, expl-0.075T,"), where is the number density after the compression and is the temperature of the gas which reaches 10 K. The gas is initially at a temperature of 10000 K, a pressure of 10 atm and a volume of 1 m. Assume that the ratio of the specific heats is constant over all temperatures and pressures and is given by y - 1.36. This question continues on the next page. 12) TURN OVER PHAS0006/2022 1
[2] [3] (d) Calculate the work required to compress the gas to a temperature of 10' K. (e) When the gas is compressed, fusion energy is released in a very short duration (10 nanoseconds) and is given by E = 10-8RVs, where V2 is the final volume of compressed gas. Calculate the energy release for an initial gas volume of 1 m. Is net energy produced in this process? (1) Determine the entropy change in the adiabatic compression stage and subsequently when fusion occurs. Assume that fusion occurs so rapidly that the energy is added to the gas at constant volume. Calculate the total change in entropy. (g) Calculate the mean and root mean square speed, as well as the average energy of the particles, before compression and just before fusion occurs. The mass of the gas (deuterium) is 2.014 unified atomic mass units. [4] [3]