The Stellar Engine Cooling Chamber · AI Generator #GEN-68471D15

Physics · thermodynamics

Problem

A futuristic spacecraft uses a stellar engine that collects high-energy photons from a nearby star and converts them to useful work. The engine's cooling chamber contains

N = 1.0 \times 10^{23}

helium atoms initially at temperature

T_1 = 2000\;\text{K}

. During operation, the chamber undergoes a carefully controlled adiabatic expansion where its volume increases by a factor of

\alpha = 8.0

. After this expansion, the chamber is brought into thermal contact with a large reservoir at temperature

T_{\text{res}} = 300\;\text{K}

until thermal equilibrium is reached. The helium can be treated as an ideal monatomic gas. (a) Find the final temperature

T_2

of the helium immediately after the adiabatic expansion. (b) Calculate the total entropy change

\Delta S_{\text{total}}

of the universe (helium + reservoir) during the subsequent thermal equilibration process. Use

k_B = 1.38 \times 10^{-23}\;\text{J/K}

and assume the reservoir is so large that its temperature remains constant.

Related theory

thermodynamics

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