Question

An ideal gas is held in a rigid container at temperature of 201∘C. Upon cooling the gas, the pressure decreases by a factor of 2.0, while the volume and the amount of gas remain constant. What must be the final temperature of the gas?

Answer 1

237 K

Step-by-step explanation:

Given that,

Initial temperature, T₁ = 201⁰C = 474 K

Let P be the initial pressure. Upon cooling the gas, the pressure decreases by a factor of 2.0, while the volume and the amount of gas remain constant.

Final pressure = P/2

The relation between the pressure and temperature is as follows :

`(P_1)/(P_2)=(T_1)/(T_2)`

Put all the known values,

`(P)/((P)/(2))=(474)/(T_2)\\\\2=(474)/(T_2)\\\\T_2=(474)/(2)\\\\T_2=237\ K`

So, the final temperature of the gas is equal to 237 K.