Question

A sample of nitrogen at 40°C has a volume of 5.0 L. At what temperature will it occupy 8.0 L?

Answer 1

Question # 82119

A sample of nitrogen at $40^{\circ}\mathrm{C}$ has a volume of 5.0 L. At what temperature will it occupy 8.0 L?

Answer:

The temperature of the nitrogen sample, which occupies $8.0\mathrm{L}$, will be $227.8^{\circ}\mathrm{C}$.

It is able to find the solution of this task, only if the pressure (P) is constant (Charles's law [1]). Otherwise, according to the ideal gas law [2], there is an infinite number of solutions:

$$\frac {P _ {1} V _ {1}}{T _ {1}} = \frac {P _ {2} V _ {2}}{T _ {2}} = const$$

So, the temperature of nitrogen will be:

$$\frac {V _ {1}}{T _ {1}} = \frac {V _ {2}}{T _ {2}} = const$$ $$T _ {2} = \frac {V _ {2} * T _ {1}}{V _ {1}} = \frac {8 l * 313 K}{5 l} = 500.8 K = 227.8 ^ {\circ} \mathrm {C}$$

References:

[1] https://en.wikipedia.org/wiki/Charles%27s_law

[2] https://en.wikipedia.org/wiki/Ideal_gas_law

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