Question 188: Thermodynamics & KTG

Question

Pressure of an ideal gas, contained in a closed vessel, is increased by $0.4 \%$ when heated by $1^{\circ} \mathrm{C}$. Its initial temperature must be:

Accepted Answer

In this scenario, we're dealing with an isochoric process, meaning the volume of the gas remains constant. For an ideal gas in an isochoric process, the pressure ($P$) is directly proportional to the temperature ($T$) in Kelvin.
The relationship can be expressed as:
$ P \propto T $
Given the percentage increase in pressure is $0.4\%$ when the temperature is increased by $1^{\circ} 	ext{C}$, we can use the relationship:
$ \frac{\Delta P}{P} = \frac{\Delta T}{T} $
Substituting the given values into the equation, we have:
$ \frac{0.4}{100} = \frac{1}{T} $
Solving for $T$, we find:
$ T = 250 \, 	ext{K} $
Therefore, the initial temperature of the gas in the vessel must be $250 \, 	ext{K}$.

Answer

2500 K

Answer

$25^{\circ} \mathrm{C}$

Answer

$250^{\circ} \mathrm{C}$

Answer

250 K

Thermodynamics & KTG

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4 \% when heated by 1^{\circ} \mathrm{C}. Its initial temperature must be:

Choose the correct answer: