Year 12: Cambridge Physics Problem (Gas and Pressure)

[johnconnor]

Guys I'm weak in heat and kinetic theory, so I'm going to need extra guide and pointers from you guys to solve this and the coming questions. Thank you.

Question:
The bulb of a constant-volume gas thermometer has a volume V and is connected by a long narrow capillary tube to a manometer, where there is a dead space of volume V/4 above the liquid. The thermometer is filled with an ideal gas at pressure p₀ and temperature T₀.

(i) Find an expression for the sensitivity of the thermometer (rate of change of pressure with temperature) at temperature T if the manomenter remains at temperature T₀.

(ii) Sketch the variation of sensitivity with temperature for the range T/K = 0 to ∞.

(iii) Show, on the same axes, sensitivity as a function of temperature for the same bulb connected to a manometer with a dead space of negligible volume (a) when filled to give the same value of p₀ at T₀, and (b) when filled with the same mass of gas as previously.

Attempt:

(i) This is the diagram of the apparatus which I think is like. Is it correct?

Or is it this one?

 

[truesearch]

It is the second diagram. The volume is kept constant by adjusting the Height of the mercury reservoir and the temperature is determined by measuring the pressure(h)

 

[johnconnor]

It is the second diagram. The volume is kept constant by adjusting the Height of the mercury reservoir and the temperature is determined by measuring the pressure(h)

Where exactly is the dead space V/4, then? Would you mind showing me a diagram with all the information labelled? Sorry for not being able to even imagine the apparatus properly. Thanks in advance!

 

[johnconnor]

Can anyone please help me with starting the question? Thank you very much in advance.