What will happen to the volume of a fixed mass of gas when its pressure and temperature (in Kelvin) are both doubled?

A. It will not change
B. It will increase
C. It will decrease
D. The change cannot be predicted

1 Answer

Answer:

No change in volume.

Explanation:

We can use the Ideal Gas Equation to solve this question:

#PV = nRT#

  • #P# is pressure in #"Pa"#
  • #V# is volume in #"m"^3#
  • #n# is number of moles of gas
  • #R# is the universal gas constant, #"8.31 J/K mol"#
  • #T# is temperature in Kelvin

In your scenario, when mass is fixed, the number of moles will be fixed, too. So we can combine both constant terms #n# and #R# to give us:

#PV = kT#

where #k# is a constant.

Now, since we want to work out how volume changes, let's put #V# on the left-hand side and move #P# to the right-hand side:

#V = (k T )/ P#

So from the equation, we can deduce that when temperature and pressure are both doubled, the Volume #V# will remain unchanged as the numerator term #T# and the denominator term #P# are both affected by a multiple of #2#, hence can be cancelled away:

#V = (k T (xx2)) /( P(xx2)) = (k T)/P#

Hope this helps!