# A gas thermometer contains 250 mL of gas at 0° C and 1.0 atm pressure. If the pressure remains at 1.0 atm, how many mL will the volume increase for every one celsius degree that the temperature rises?

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I don't understand this part "for every one celsius degree"

I don't understand this part "for every one celsius degree"

##### 1 Answer

Here's what I got.

#### Explanation:

The problem states that the pressure remains *unchanged*, so right from the start, you should know that you can use **Charles' Law** to calculate the change in volume associated with a

#color(blue)(ul(color(black)(V_1/T_1 = V_2/T_2)))#

Here

#V_1# and#T_1# represent the volume and the absolute temperature of the gas at an initial state#V_2# and#T_2# represent the volume and the absolute temperature of the gas at a final state

Now, it's very important to remember that you **must** work with *absolute temperatures* here, i.e. with temperatures expressed in *Kelvin*.

In your case, the gas starts at

#0^@"C" = 0^@"C" + 273.15 = "273.15 K"#

When the temperature of the gas increases by

#0^@"C" + 1^@"C" = 1^@"C" -># the temperatueincreasesby#1^@"C"#

which is

#1^@"C" = 1^@"C" + 273.15 = "274.15 K"#

Similarly, you will have

#"273.15 K" + "1 K" = "274.15 K" -># the temperatureincreasesby#"1 K"#

So, you must determine the change in volume that accompanies a

Rearrange the equation to solve for

#V_1/T_1 = V_2/T_2 implies V_2 = T_2/T_1 * V_1#

Plug in your values to find

#V_2 = (274.15 color(red)(cancel(color(black)("K"))))/(273.15color(red)(cancel(color(black)("K")))) * "250 mL" = "250.9 mL"#

So the volume of the gas **increased** by

#overbrace("250.9 mL")^(color(blue)("at 274.15 K" = 1^@"C")) - overbrace("250 mL")^(color(blue)("at 273.15 K" = 0^@"C")) = "0.9 mL"#

Notice what happens when you increase the temperature from

#V_2 = (275.15 color(red)(cancel(color(black)("K"))))/(274.15 color(red)(cancel(color(black)("K")))) * "250.9 mL" = "251.8 mL"#

The volume of the gas **increased** by

#overbrace("251.8 mL")^(color(blue)("at 275.15 K" = 2^@"C")) - overbrace("250.9 mL")^(color(blue)("at 274.15 K" = 1^@"C")) = "0.9 mL"#

You can thus say that with every **increase** in temperature, the volume of the gas **increases** by

If you were to draw a graph of this relationship, you'd end up with a straight line that goes **up** as you move **right**, i.e. the volume *increases* by *increase* in temperature.