Question #25887

A balloon is filled with hydrogen at 26oC. The balloon expands until the pressure is equal to the barometric pressure of 750 Torr. The balloon rises to an altitude of 6000 ft, where the pressure is 600 Torr and the temperature is 14oC. What is the change in the volume of the balloon as it ascends to 6000 ft ?

Expert's answer

This question can be solved by using the ideal gas law:

PV = nRT

But even if you have two different conditions the amount is the same (R is const), so:

P_{1}V_{1} = nRT_{1}

n = P_{1}V_{1}/RT_{1}

n = P_{2}V_{2}/RT_{2}

P_{1}V_{1}/RT_{1} = P_{2}V_{2}/RT_{2}

P_{1}V_{1}/T_{1} = P_{2}V_{2}/T_{2}

If starting volume is V_{1}:

T_{1} = 26 C

T_{2} = 14 C

P_{1} = 750 Torr

P_{2} = 600 Torr

750 Torr V_{1}/26 C = 600 Torr V_{2}/14 C

28.85 V_{1 }= 42.86 V_{2}

0,67*V_{1} = V_{2}

PV = nRT

But even if you have two different conditions the amount is the same (R is const), so:

P

n = P

n = P

P

P

If starting volume is V

T

T

P

P

750 Torr V

28.85 V

0,67*V

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