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

Answer:

237 K

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 :

$\dfrac{P_1}{P_2}=\dfrac{T_1}{T_2}$

Put all the known values,

$\dfrac{P}{\dfrac{P}{2}}=\dfrac{474}{T_2}\\\\2=\dfrac{474}{T_2}\\\\T_2=\dfrac{474}{2}\\\\T_2=237\ K$

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