# Question #14dea

Mar 11, 2017

$1.1 \cdot P$

#### Explanation:

The idea here is that when the volume and the number of moles of gas are being kept constant, the pressure of the gas is directly proportional to its temperature, as described by Gay Lussac's Law.

Mathematically, this is written as

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}}}}$

Here

• ${P}_{1}$, ${T}_{1}$ are the pressure and temperature of the gas at an initial state
• ${P}_{2}$ and ${T}_{2}$ are the pressure and temperature of the gas at final state

Now, it's important to realize that the temperature of the gas must be expressed in Kelvin, not in degrees Celsius. This means that you are going to have to convert the two temperatures given to you by using

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{T \left[\text{K"] = t[""^@"C}\right] + 273.15}}}$

So, you know that the initial pressure of the gas is equal to $P$, so

${P}_{1} = P$

Rearrange the equation to solve for ${P}_{2}$

$\frac{P}{T} _ 1 = {P}_{2} / {T}_{2} \implies {P}_{2} = {T}_{2} / {T}_{1} \cdot P$

Plug in your values to find

${P}_{2} = \left(\left(57 + 273.15\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{K"))))/((27 + 273.15)color(red)(cancel(color(black)("K}}}}\right) \cdot P = \frac{330.15}{300.15} \cdot P$

If you want, you can simplify this to get

${P}_{2} = 1.1 \cdot P$

As you can see, the pressure of the gas increases as a result of the increase in temperature.