# Question #14dea

##### 1 Answer

#### Answer:

#### 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

#color(blue)(ul(color(black)(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

#color(blue)(ul(color(black)(T["K"] = t[""^@"C"] + 273.15)))#

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

#P_1 = P#

Rearrange the equation to solve for

#P/T_1 = P_2/T_2 implies P_2 = T_2/T_1 * P#

Plug in your values to find

#P_2 = ((57 + 273.15)color(red)(cancel(color(black)("K"))))/((27 + 273.15)color(red)(cancel(color(black)("K")))) * P = 330.15/300.15 * P#

If you want, you can simplify this to get

#P_2 = 1.1 * P#

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