Question

At 27°c, a gas is compressed isothermally to half of its volume. to what temperature it must now be heated isobarically so that gas occupies just its original volume? o

Answer 1

330∘C

Assuming an ideal gas and that we are at constant pressure and mols of ideal gas, we construct two ideal gas states:

PV1=nRT1
PV2=nRT2

Solving for nRP, we realize...

V1T1=V2T2

which is Charles law, relating volume and temperature changes at constant pressureand mols of gas .

Designate the original volume as V. Note that if we are sloppy and do not change temperature units, we have failed miserably.

T2=(V2V1)T1

=V0.5V(27∘C)

⇒T2=54∘C−−−−−

which is completely incorrect... What we should have done is recognize that 27∘C+273.15→300.15 K. Hence, what we should have written is:

T2=10.5(300.15 K)

= 6.003×102K

or 327.15∘C→330∘C to two sig figs. That is, the KELVIN temperature is doubled, just as we expected when we wish to double the volume