Question

During an experiment you seal a small quantity of ideal gas in a flexible container of volume V₀ and place it an a barometric chamber.

When the gas was sealed it was at a temperature of 20°C.

The absolute pressure in chamber is reduced by 20% and the chamber is chilled to 0.0°C.

What is the ratio of the volume of the sample now V, to the original volume of the sample, V₀? (i.e., find V/V₀) 

Answer 1

Find V/V₀ using the combined gas law. We know that the final pressure is 0.8 of the initial, i.e., $P=0.8P_0.$ Do not forget that the temperature must be converted to kelvins:

$$\frac{P_0V_0}{T_0}=\frac{PV}{T},\\\space\\ \frac{V}{V_0}=\frac{P_0T}{PT_0}=\frac{P_0\cdot(273+0)}{(0.8P_0)(273+20)}=1.16.$$