The Hot Air Balloon Temperature Gauge · AI Generator #GEN-F500F014

Physics · thermodynamics

Problem

A hot air balloon pilot uses an ingenious temperature measurement system. The balloon envelope contains a small sealed glass bulb with volume V0=50.0  cm3V_0 = 50.0\;\text{cm}^3 that was filled with air at ground level where T0=20.0°CT_0 = 20.0°\text{C} and pressure p0=1.01×105  Pap_0 = 1.01 \times 10^5\;\text{Pa}. The bulb is connected to a narrow vertical glass tube of uniform cross-sectional area A=2.00  mm2A = 2.00\;\text{mm}^2. Initially, a small mercury plug of length L0=5.00  cmL_0 = 5.00\;\text{cm} sits in the tube, sealing the air in the bulb. When the balloon is heated for launch, the trapped air expands and pushes the mercury plug upward. The pilot observes that the mercury plug has moved up by Δh=8.50  cm\Delta h = 8.50\;\text{cm} from its initial position. Assuming the pressure inside the balloon envelope (and thus the pressure on the mercury plug) remains constant at atmospheric pressure throughout the heating process, what is the new temperature of the air inside the bulb?

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