HARD PROBLEM

Question

A gas sample experiences a pressure increase from 1.0 atm to 1.2 atm. If the temperature of the gas at the lower pressure was 200 K, what is the temperature of the gas at the higher pressure? Assume that the volume of the gas does not change

Answer 1

Hi Mylah,

 

You can use the Ideal Gas Law formula to see the interplay between the different variables: PV=nRT where P is the Pressure, V the volume, n the number of moles of gas, R the Gas constant, and T the temperature in Kelvin.

 

Let's set up the initial scenario: P₁V=nRT₁

 and also for the final scenario: P₂V=nRT₂

 

Now, we can setup a ratio between the two scenarios: [P₁V=nRT₁ / P₂V=nRT₂]

We know that the Volume (V) doesn't change, and similarly number of moles of gas (n) doesn't change.  We also now that R is the same value in both cases.  Therefore, we can V, n, and R cancel out in the ratio above.  We are left with P₁/P₂=T₁/T₂.

Plugin the values for P₁, P₂, and T₁ to solve for T₂ through cross multiplication.  You have [1atm/1.2atm] = [200K/T₂] and therefore T₂ = 240K.  Note that P and T are directly proportional in the Ideal Gas Law formula.  So, as the pressure increases, we expect the temperature to increase too.  In this case, we see that it does!

 

Hope this helps,

Babita