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# A gas thermometer is envisaged where by the change in V is used as a measure of temp change. At 1 atm what would the change in V as 42g of nitrogen gas goes from 15 to 20C? what difficulties can you envisage in using this system to measure room temp?

The volume of the gas will increase by a factor of ##1.073##.

The idea here is that you can use to calculate the change in volume caused by the given change in temperature, provided of course that the pressure **stays constant**.

The mass of nitrogen gas is not relevant here. This mass is equivalent to a number of moles of gas, but since the quantity of nitrogen gas remains **unchanged**, you don't have to worry about exactly how many moles you have in there.

So, you know that when pressure and number of moles of gas are **constant**, **volume** and **temperature** have a direct relationship.

Simply put, when temperature increases, the volume of the gas **Increases** as well. SImilarlly, when temperature decreases, the volume of the gas **decreases** as well.

You can thus say that

##color(blue)(|bar(ul(color(white)(a/a)V_1/T_1 = V_2/T_2color(white)(a/a)|)))" "##, where

##V_1##, ##T_1## - the volume and **absolute temperature** of the gas at an initial state
##V_2##, ##T_2## - the volume and **absolute temperature** of the gas at a final stat

It's very important to realize that you're dealing with **absolute temperature**, which is temperature expressed in Kelvin, so make sure that you convert your two values before using the equation.

Your goal here is to solve for ##V_2##, the final volume of the gas

##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 = ( (273.15 + 20)color(red)(cancel(color(black)("K"))))/((273.15 + 15)color(red)(cancel(color(black)("K")))) * V_1##

##V_2 = 1.073 * V_1##

You can thus say that the volume of the gas will **increase** by a factor of ##1.073## as a result of the temperature increasing from ##15^@"C"## to ##20^@"C"##.