If i initially have a gas with a pressure of 84kPa and a temperature of 35 Celsius and I heat it up to 230 degrees Celsius, what will the new pressure be?  Assume that the volume of the container...

If i initially have a gas with a pressure of 84kPa and a temperature of 35 Celsius and I heat it up to 230 degrees Celsius, what will the new pressure be?  Assume that the volume of the container is constant.

 

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For this problem, we can use the gas relationship between pressure and temperature at constant volume. This gas law is also called as the Gay-Lussac’s Law which states that:

P is directly proportional to T; as the pressure of the container increased, the total temperature will increase.

``P = k T` `

``k = (P)/(T)`

Now, for comparing the same substance at two different conditions, this can be expressed as:

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

OR

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

From this we can solve the problem.

Given:

P1 = 84 kPa  -> initial pressure

T1 = 35 + 273.15 = 308.15K -> initial temperature

T2 = 230 + 273.15 = 503.15 K -> final temperature

P2 = x (unknown) -> final pressure

Substitute the given values and solve for the unknown:

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

`(84)(503.15) = (x)(308.15)`

`X = (84*503.15)/(308.15)`

X = 137 kPa = Pressure at 230 degrees Celsius

 

 

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