Question

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.

Answer 1

By the ideal gas law, PV/T = constant. Use this fact to answer your question.

Answer 2

So, since v isnt given, we can just ignore it. So a comparison like this would be appropriate: \[P_{1}/2 = P_{2}/4\rightarrow 2P _{1}=P _{2}\]

Answer 3

So the answer is then A.2P! right?

Answer 4

Not exactly, be careful about T! This has to be the absolute temperature, i.e. the temperature in Kelvin.

Answer 5

well i just meant 20c and 40c

Answer 6

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

Answer 7

But would my above proportion hold true?

Answer 8

No, definitely not.

Answer 9

No, because \[T_1 = (20 + 273) K = 293 K\]\[T_2 = (40 + 273) K = 313 K\] and therefore \[\frac{P_2}{P_1} = \frac{T_2}{T_1} = \frac{313 K}{293 K} < 2\]

Answer 10

So how does that use PV/T

Answer 11

PV/T is a constant. Hence if V is also a constant, then P/T is a constant also.

Answer 12

So if we can not use the relation p1/293k = p2/313k, Im not sure how to go about with a solution

Answer 13

...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.

Answer 14

We are trying to find P2, and in our answers we can use P1

Answer 15

So why not muliply P1 to the other side?

Answer 16

P2/P1 = T2/T1

Answer 17

-> P2 = P1T2/T1

Answer 18

P2 = 313P2/293 -> P2 = 1.068ishP2

Answer 19

This is the same answer I could get with my original proportion of P1/293 = P2/313, no?

Answer 20

Mess up the P2 a bit in a few posts above.

Answer 21

I just needed to convert

Answer 22

Ok, I get what you guys were saying, haha. thanks!