Question

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?

Answer 1

The answer is `1000K`.

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

`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 = 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.