# A cylinder with a volume of 0.03 m3 contains gas under a pressure of 1.35 * 10 ^ 6 Pa at a temperature of 455 C.

**A cylinder with a volume of 0.03 m3 contains gas under a pressure of 1.35 * 10 ^ 6 Pa at a temperature of 455 C. What volume does this gas take under normal conditions (temperature 273 K, pressure 100 kPa?)**

Given:

V = 0.03 m3 (cubic meter) – initial gas volume;

P = 1.35 * 106 Pascal = 1,350,000 Pascal – initial gas pressure;

T = 455 ° Celsius = 728 ° Kelvin – initial gas temperature;

P1 = 100 kPa = 100000 Pascal – normal pressure;

T1 = 273 ° Kelvin – normal temperature.

It is required to determine V1 (m3) – what volume the gas will occupy under normal conditions.

Since the condition of the problem is not specified, we believe that the gas is ideal. Then, to determine the volume of gas under normal conditions, you must use the following formula:

P * V / T = P1 * V1 / T1;

P * V * T1 / T = P1 * V1;

V1 = P * V * T1 / (P1 * T) = 1,350,000 * 0.03 * 273 / (728 * 100,000) =

= 135 * 0.03 * 273 / (728 * 10) = 1105.65 / 7280 = 0.15 m3 (the result has been rounded to one hundredth).

Answer: under normal conditions, the gas will occupy a volume of 0.15 m3.