Answer: The original temperature was
[tex]T_{1}=126.51K[/tex]
Explanation:
Let's put the information in mathematical form:
[tex]V_{1}=12.7m^{3}[/tex]
[tex]T_{1}=?[/tex]
[tex]V_{2}=32.5m^{3}[/tex]
[tex]T_{2}=323K[/tex]
[tex]P_{1}=P_{2}=3atm[/tex]
If we consider the helium as an ideal gas, we can use the Ideal Gas Law:
[tex]PV=nRT[/tex]
were R is the gas constant. And n is the number of moles (which we don't know yet)
From this, taking [tex]R=0.08205746\frac{atm.l}{mol.K}[/tex], we have:
[tex]n=\frac{P_{2}V_{2}}{RT_{2}}[/tex]
⇒[tex]n=3.67mol[/tex]
Now:
[tex]T_{1}=\frac{P_{1}V_{1}}{nR}[/tex]
⇒[tex]T_{1}=126.51K[/tex]
