# Conversion factors for volume changes in a gas?

If a balloon containing 3000 L of gas at 39 degrees C and 99 kPa rises to an altitude where the pressure is 45.5 kPa and the temperature is 16 degrees C, the volume of the balloon under these new conditions would be calculated using which of the following conversion factor ratios:

a. 3000 L x 99 kPa x 39 degrees C / 45.4 x 16 deg C

b. 3000 L x 45.5 kPa X 289 K / 99 kPa x 312 K

c. 3000 L x 99 kPa x 289 K / 45.5 kPa x 312

d. 3000 L x 99 kPa x 312 K / 45.5 x 289 K

Relevance

from the ideal gas law... the answer SHOULD look like this

.. P1V1 / T1 = P2V2 / T2

.. V2 = V1 * (P1 / P2) * (T2 / T1)

.. V2 = 3000L * (99 kPa / 45.5 kPa) * ( (16+273.15 K) / (39 + 273.15K) ) = __ L

.. V2 = 3000L * (99 kPa / 45.5 kPa) * (289 K / 312K)

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now let's look at your choices

.. (a) INCORRECT

.. .. . .V2 = 3000 L * (99 kPa / 45.5 kPa) * (39°C / 16°C)

.. .. .. V2 = V1 * (P1 / P2) * (T1 / T2)..

.. .. . . T1/T2 is inverted AND T must be absolute!

.. (b) INCORRECT

.. . .. .V2 = 3000 L * (45.5 kPa / 99 kPa) * (289K / 312K)

.. . . ..V2 = V1 * (P2 / P1) * (T2 / T1)

.. . . . P2/P1 is inverted

.. (c) CORRECT

.. .. .. V2 = 3000 L * (99 kPa / 45.5 kPa) * (289K / 312K)

.. .. ..V2 = V1 * (P1 / P2) * (T2 / T1)

.. (d) INCORRECT

.. .. . ..V2 = 3000 L * (99 kPa / 45.5 kPa) * (312K / 289K)

.. . .. ..V2 = V1 * (P1 / P2) * (T1 / T2)

.. .. .. .T1/T2 is inverted

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c. is the correct choice

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• Thank you, Dr. W.

• very welcome

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