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A gas in a balloon expands from 2L to 3L against 2 atm of pressure, what is the change in temperature relative to the initial temperature?

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2 Answers

Since the pressure is constant, V/T = constant

V1/T1 = V2/T2

T2/T1 = V2/V1 = 3/2

(T2-T1)/T1 = 3/2 - 1 = 1/2

It means that the temperature is increased by 1/2 of its initial temperature.

The general equation governing changes in fixed-quantity gasses is

  P1V1          P2V2
---------  =  -------
   T1            T2

This is what is known as the "combined gas law" because it covers the other known laws with separate names:

  • Boyle's Law - constant temperature - P1V1 = P2V2
  • Gay-Lussac's Law - constant volume - P1T2 = P2T1
  • Charles's Law - constant pressure - V1T2 = V2T1

In this case, since the pressure is constant (2 atm) but volume and temperature are changing, we can use Charles's Law:

V1T2 = V2T1
(2)(T2) = (3)(T1)
T2 = 3/2 T1

So the final temperature is 1.5x the initial temperature.  Note specifically that both the initial and final temperature in this equation must be measured in Kelvins (absolute temperature) - you cannot use Fahrenheit or even Celsius, as they are not the natural temperature scales.  If the problem gives initial temperatures in either °F or °C then you must convert to Kelvin first:

K = (5/9)(F - 32) - 273.15
   = C - 273.15

where F is degrees Fahrenheit and C is degrees Celsius.

Comments

You didn't answer "the change in temperature relative to the initial temperature".

I disagree.

At worst, I think that is a matter of interpretation on an ambiguous question, and a matter of semantics.  Does "the change" refer to an additive change or a multiplicative change.  Both are "relative to" the initial temperature.  IMO, most questions of this sort expect a multiplicative factor, not an additive one.  

I saw that you had posted an additive answer, so I chose to go with the other option.  But even so, when you say "it increased by 1/2 of it's original temperature" that is no different than when I say "the final temperature is 1.5x the initial temperature".  It's just you stated the change as an additive term, and I stated it as a multiplicative factor.  It's the same thing, just the same as saying "my bank account went up by 50%" vs "my bank account is 1.5 time what it used to be".... the only difference is in the semantics, but it's the same answer.