Question

Two flasks of equal volume connected by a narrow tube of negligible volume are filled with nitrogen gas. When both are immersed in boiling water, the gas pressure inside the system is $\text{0}\text{.5 atm}$ . The pressure of the system when one of the flasks is immersed in an ice water mixture keeping the other in boiling water, is?
(A) $\text{0}\text{.25 atm}$
(B) $\text{0}\text{.5 atm}$
(C) $\text{0}\text{.433 atm}$
(D) $\text{0}\text{.72 atm}$

Answer 1

This problem is based on the “Amonton’s Law” which states that the pressure of a fixed mass of gas is directly proportional to its temperature on the Kelvin Scale, provided that the volume of the gas remains constant throughout”.

Complete step by step solution:
According to the question, it is given that the two flasks have equal volume are connected together by a narrow tube of negligible volume and are filled with nitrogen gas, so it can be taken that the volume of the system remains constant during the process.
The initial pressure of the system is: $\text{0}\text{.5 atm}$
The temperature of boiling water = $\text{273 + 100 = 373 K}$ , as the temperature of the boiling water = $\text{100}{{\text{ }}^{\text{0}}}\text{C}$ .
The temperature of ice cold water = $\text{273 + 0 = 273 K}$ , as the temperature of the boiling water = $\text{0}{{\text{ }}^{\text{0}}}\text{C}$ .
The average temperature of the flasks when the temperatures are equal will be:
$\dfrac{\text{373 + 273 }}{\text{2}}\text{= }\dfrac{\text{646}}{\text{2}}\text{= 323 K}$
From the Amonton’s Law we can say that, $\text{P }\infty \text{ T}$
$\Rightarrow \dfrac{{{\text{P}}_{\text{1}}}}{{{\text{T}}_{\text{1}}}}\text{ = }\dfrac{{{\text{P}}_{\text{2}}}}{{{\text{T}}_{\text{2}}}}$
Here we know the values of ${{\text{P}}_{\text{1}}}=\text{0}\text{.5 atm}$ , ${{\text{T}}_{\text{1}}}\text{ = 373 K}$ , and ${{\text{T}}_{2}}\text{ = 273 K}$ , therefore, ${{\text{P}}_{2}}=\dfrac{{{\text{P}}_{\text{1}}}\times {{\text{T}}_{\text{2}}}}{{{\text{T}}_{\text{1}}}}\text{ }$
${{\text{P}}_{\text{2}}}\text{=}\dfrac{\text{0}\text{.5 }\\!\\!\times\\!\\!\text{ 323}}{\text{373}}\text{ = 0}\text{.433 atm}$
Hence the pressure of the system when one of the flasks is immersed in an ice water mixture keeping the other in boiling water, is $\text{ 0}\text{.433 atm}$ .
Hence, option C is correct.

Note:
Just like the Amonton’s law of pressure, the Charles’ law relates the volume of a fixed mass of gas with the temperature in the Kelvin scale when the pressure of the gas is kept constant under those conditions and states that the volume of the gas is directly proportional to the temperature of the gas. The Boyles’ Law relates the pressure of a fixed mass of gas with the volume of that gas and states that the pressure of the gas is inversely proportional to the volume of a fixed mass of gas under constant temperature.