anonymous
  • anonymous
A fixed amount of ideal gas is held in a rigid container that expands negligibly when heated. At 20°C the gas pressure is P. If we add enough heat to increase the temperature from 20°C to 40°C, the pressure will be: A. equal to 2P B. less than 2P C. impossible to determine since we do not know the number of moles of gas in the container D. greater than 2P or E. impossible to determine since we do not know the volume of gas in the container.
Physics
jamiebookeater
  • jamiebookeater
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JamesJ
  • JamesJ
By the ideal gas law, PV/T = constant. Use this fact to answer your question.
anonymous
  • anonymous
So, since v isnt given, we can just ignore it. So a comparison like this would be appropriate: \[P_{1}/2 = P_{2}/4\rightarrow 2P _{1}=P _{2}\]
anonymous
  • anonymous
So the answer is then A.2P! right?

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anonymous
  • anonymous
Not exactly, be careful about T! This has to be the absolute temperature, i.e. the temperature in Kelvin.
anonymous
  • anonymous
well i just meant 20c and 40c
JamesJ
  • JamesJ
In the ideal gas law, we have to use temperature in Kelvin. Otherwise we would very quickly have problems. For example, given that P/T is a constant, suppose T was in Celcius and we wanted to know the pressure for a balloon of hydrogen gas going from 1 atm at 20 C to -10 C. Then we'd have \[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \implies P_2 = \frac{P_1}{T_1} T_2 = \frac{1}{20}(-10) = -1/2 \] a negative pressure! Which is clearly nonsense. Hence you need to convert the temperatures 20 and 40 C into an absolute temperature scale, Kelvin. E.g. 20 C = 273 + 20 K = 293 K
anonymous
  • anonymous
But would my above proportion hold true?
JamesJ
  • JamesJ
No, definitely not.
anonymous
  • anonymous
No, because \[T_1 = (20 + 273) K = 293 K\]\[T_2 = (40 + 273) K = 313 K\] and therefore \[\frac{P_2}{P_1} = \frac{T_2}{T_1} = \frac{313 K}{293 K} < 2\]
anonymous
  • anonymous
So how does that use PV/T
JamesJ
  • JamesJ
PV/T is a constant. Hence if V is also a constant, then P/T is a constant also.
anonymous
  • anonymous
So if we can not use the relation p1/293k = p2/313k, Im not sure how to go about with a solution
JamesJ
  • JamesJ
...and \[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \implies \frac{P_2}{P_1} = \frac{T_2}{T_1} \] It is this second form that chris has used in his solution. Think about the algebra here a bit more before being so reflexive.
anonymous
  • anonymous
We are trying to find P2, and in our answers we can use P1
anonymous
  • anonymous
So why not muliply P1 to the other side?
anonymous
  • anonymous
P2/P1 = T2/T1
anonymous
  • anonymous
-> P2 = P1T2/T1
anonymous
  • anonymous
P2 = 313P2/293 -> P2 = 1.068ishP2
anonymous
  • anonymous
This is the same answer I could get with my original proportion of P1/293 = P2/313, no?
anonymous
  • anonymous
Mess up the P2 a bit in a few posts above.
anonymous
  • anonymous
I just needed to convert
anonymous
  • anonymous
Ok, I get what you guys were saying, haha. thanks!

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