A gas in a rigid container is heated from 100 degrees Celsius to 500 degrees Celsius. What will happen to the pressure of the gas?

In this scenario, the behavior of the gas can be understood through the ideal gas law, which relates pressure (P), volume (V), temperature (T), and the number of moles (n) of gas in the equation PV = nRT. Since the gas is contained in a rigid container, the volume remains constant.

When the temperature of the gas increases from 100 degrees Celsius to 500 degrees Celsius, it is important to convert these temperatures to Kelvin to use in the gas law calculations. The corresponding temperatures in Kelvin are 373 K and 773 K, respectively.

According to the ideal gas law, if the volume and the number of moles of gas remain constant, the pressure of the gas is directly proportional to the absolute temperature (in Kelvin). This means that as the temperature increases, the pressure will also increase.

To quantify this increase, we can look at the ratio of the final temperature to the initial temperature:

[

\text{Pressure Ratio} = \frac{P_f}{P_i} = \frac{T_f}{T_i} = \frac{773 , \text{K}}{373 , \text{K}} \approx 2.07

]