The Pressurized Coffee Bean Roaster · AI Generator #GEN-D4676B8C

Physics · thermodynamics

Problem

A specialty coffee roaster uses a sealed cylindrical chamber to roast beans under controlled pressure. The chamber has volume

V = 0.050\;\text{m}^3

and initially contains air at atmospheric pressure

P_0 = 1.01 \times 10^5\;\text{Pa}

and temperature

T_0 = 293\;\text{K}

. During roasting, the chamber is heated to

T_f = 473\;\text{K}

while being supplied with additional air to maintain constant density. The coffee beans occupy negligible volume compared to the chamber. After roasting, the air supply is cut off and the chamber is allowed to cool back to room temperature

T_0

while remaining sealed. What is the final gauge pressure (pressure above atmospheric) in the chamber after cooling?

Related theory

thermodynamics

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