Question

consider a gas with contanst mass.if P reduced to half and temperature doubled.what will happen to the volume of gas?

Answer 1

By the ideal gas law PV/T is a constant. Hence if P is halved and T doubled, the only way that can happen and PV/T be constant is if V does what?

Answer 2

a.4v
b.2v^2
c.v/4
d.8v

Answer 3

\[ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \]
Now
\[ P_2 = (1/2)P_1 \]
and
\[ T_2 = 2T_1 \]
Hence
\[ \frac{P_2V_2}{T_2} = \frac{(1/2)P_1V_2}{2T_1} = \frac{P_1V_2}{4T_1} \]

Hence V_2 must be what multiple of V_1 ?

Answer 4

i dont understand..=(

Answer 5

What's the ideal gas law?

Answer 6

What do you know about the relationship between pressure, volume and temperature of a gas?

Answer 7

PV=nRT

Answer 8

Right. Notice first that
PV/T = nR.

So if the mass of the gas remains the same, it must be that for any change in P, V or T,
PV/T is equal to the same number because nR doesn't change.

Hence for a configuration of the gas with a pressure P_1, a volume V_1 and a temperature T_1; and then another configuration of the gas with a potentially different pressure P_1, a potentially different volume V_2 and a potentially different temperature T_2, it must be that
\[ P_1V_1/T_1 = P_2V_2/T_2 \]

If that makes sense, then read again what I wrote above. If it doesn't make sense, ask me about it.