A gas originally at a temperature of 23.13C. What temperature must it be heated to triple its volume with constant pressure? Answer in celsius units

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Answer 1 · 2018-05-11T14:25:51

Recall the relationship between those parameters,

$P V = n R T$ $PV = nRT$

$\Rightarrow \frac{V_{1}}{T_{1}} = \frac{n R}{P} = \frac{V_{2}}{T_{2}}$ $=>V_1/T_1 = (nR)/P = V_2/T_2$

$\Rightarrow \frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ $=> V_1/T_1 = V_2/T_2$

Generally,

$V \propto T$ $V propto T$

So we expect an increase in temperature to accompany the increase in volume. If the volume increases by a factor of three, so must the temperature.

Hence,

$3V_1 = 3T_1 = T_2 approx 69.39°"C"$

is the temperature at which this gas (all else constant) will expand to three times its original volume.