Question

The gas inside of a container exerts `"84 Pa"` of pressure and is at a temperature of `"320 K"`. If the pressure in the container changes to `"64 Pa"` with no change in the container's volume, what is the new temperature of the gas?

Answer 1

One way to do this is to use the ideal gas law and derive an equation.

`PV = nRT`

where:

• `P` is the pressure in `"Pa"`, let's say. It doesn't matter in this case.
• `V` is the volume in `"L"`.
• `n` is the number of `\mathbf("mol")`s of gas
• `R` is the universal gas constant, which will be, based on our units, `"0.083145 L"cdot"bar/mol"cdot"K"`.
• `T` is the temperature in units of `"K"`.

Then, we would say that if state `1` represented an initial state and state `2` a final state, we have `P_1 -> P_2` and `T_1 -> T_2`, but `V_1 = V_2 = V` and `n_1 = n_2 = n`.

With this information we get two ideal gas law relationships:

`P_1V = nRT_1`
`P_2V = nRT_2`

Therefore, to find the new temperature, we can divide these to get:

`P_1/P_2 = T_1/T_2`

`\mathbf(T_2 = T_1*P_2/P_1)`

So, now that we have the final equation, we can acquire `T_2` for an ideal gas.

`color(blue)(T_2) = "320 K" xx (84/64)`

`=` `color(blue)("420 K")`