Question

a gas thermometer measure temperature by measuring the pressure of a gas inside the fixed volume container a thermometer reads a pressure of 248 torr at 0 degrees Celsius what is the temperature when the thermometer reads a pressure of 345 torr

Answer 1

Hello!

a gas thermometer measure temperature by measuring the pressure of a gas inside the fixed volume container a thermometer reads a pressure of 248 torr at 0 degrees Celsius what is the temperature when the thermometer reads a pressure of 345 torr

We have the following information:

P1 (initial pressure) = 248 torr

T1 (initial temperature) = 0 ºC (in Kelvin)

TK = TºC + 273.15 → TK = 0 + 273.15 → T1 (initial temperature) = 273.15 K

P2 (final pressure) = 345 torr

T2 (final temperature) = ? (in Kelvin)

According to the Law of Charles and Gay-Lussac in the study of gases, we have an isochoric (or isovolumetric) transformation when its volume remains constant or equal, then we will have the following formula:

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

$\dfrac{248}{273.15} = \dfrac{345}{T_2}$

$248*T_2 = 345*273.15$

$248\:T_2 = 94236.75$

$T_2 = \dfrac{94236.75}{248}$

$T_2 = 379.9868952... \to \boxed{\boxed{T_2 \approx 380\:K}}\end{array}}\qquad\checkmark$

If you want the solution in Celsius Temperature, we have:

TC = TK - 273.15

TC = 380 - 273.15

TC =  106.85 → Temperature = 106.85 ºC

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I Hope this helps, greetings ... Dexteright02! =)