5.00 L of a gas is collected at 100 K and then allowed to expand to 50.0 L. What is the new temperature in order to maintain the same pressure?

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5.00 L of a gas is collected at 100 K and then allowed to expand to 50.0 L. What is the new temperature in order to maintain the same pressure?

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Answer 1 · 2014-12-16T10:30:11

The answer is $1000 K$ $1000K$ .

According to Charles' law, the volume of a gas is proportional to its temeprature (in $K$ $K$ ).

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

Before doing any calculations, one should try and predict what the answer could look like. Now, since the volume increases by a factor of 10, we should expect the temperature to increase significantly in order to compensate for the larger volume - in the scope of keeping the pressure constant. Indeed,

$T_{2} = \frac{V_{2}}{V_{1}} \cdot T_{1} = \frac{50.0 L}{5.00 L} \cdot 100 K = 1000 K$ $T_2 = V_2/V_1 * T_1 = (50.0L)/(5.00L) * 100K = 1000K$

Since volume and temperature are proportional to each other, the increase in temperature must match the increase in volume.

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5.00 L of a gas is collected at 100 K and then allowed to expand to 50.0 L. What is the new temperature in order to maintain the same pressure?

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