A helium-filled balloon escapes a child's hand at sea level and 23.0 C. When it reaches an altitude of 3000 m, where the temperature is 4.4 C and the pressure is only 0.71 atm, how will its volume compare to that at sea level?

1 Answer
SCooke
Sep 17, 2016

It will be 1.5 times larger.

Explanation:

The altitude itself is irrelevant. The ideal gas law states
#(P_1 * V_1)/T_1 = (P_2 * V_2)/T_2# The temperatures must be in ‘K for the ratio to be correct.

#(1atm * V_1)/296 = (0.71atm * V_2)/277.4#

#V_1/V_2# = 277.4/296 * 0.71 ; #V_1/V_2# = 0.665

Therefore, the volume at 3000m is 1/0.665 = 1.5 times larger than at sea level.

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