Answer:
Approximately [tex]52\; {\rm ^\circ C}[/tex] (approximately [tex]325\; \rm K[/tex]), assuming that nitrogen is an ideal gas.
Explanation:
Let [tex]R[/tex] denote the ideal gas constant. By the ideal gas law, the following equation would relate these quantities:
[tex]P \cdot V = n \cdot R \cdot T[/tex].
Rearrange this equation to obtain an expression for [tex]T[/tex]:
[tex]\begin{aligned}T &= \frac{P \cdot V}{n \cdot R}\end{aligned}[/tex].
Look up the ideal gas constant: [tex]R \approx 8.314\; \rm Pa \cdot m^{3} \cdot K^{-1} \cdot mol^{-1}[/tex].
Convert each measurements from the question to standard units:
Substitute these values into the expression for [tex]T[/tex]:
[tex]\begin{aligned}T &= \frac{P \cdot V}{n \cdot R} \\ &\approx \frac{101.3\times 10^{5}\; \rm Pa \times 0.080\; \rm m^{3}}{3.0\; \rm mol \times 8.314\; \rm Pa \cdot m^{3} \cdot K^{-1} \cdot mol^{-1}} \\ &\approx 324.91\; \rm K\end{aligned}[/tex].
Convert the unit of this temperature to degrees celsius:
[tex]\begin{aligned} & 324.91\; \rm K \\ =\; & (324.91 - 273.15)\; {\rm ^\circ C} \\ \approx \; & 52\; {\rm ^\circ C} \end{aligned}[/tex].
