Question

The mercury manometer shown in the figure(Figure 1) is attached to a gas cell. The mercury height h is 120 mm when the cell is placed in an ice-water mixture. The mercury height drops to 30 mm when the device is carried into an industrial freezer.
Hint: The right tube of the manometer is much narrower than the left tube. What reasonable assumption can you make about the gas volume

What is the freezer temperature

Answer 1

Set up the ideal gas law for both situations:
P1*V = n*R*T1
P2*V = n*R*T2

Amount of gas is unchanged, and any change in volume is neglected.

Gather and separate variables:
P1/T1 = n*R/V
P2/T2 = n*R/V

Equate the parts which are unchanged:
P1/T1 = P2/T2

Solve for T2:
T2 = T1*P2/P1

NOW, to discuss the units:
All temperatures must be in absolute scales (Kelvin or Rankine), and obviously both the same units.
All pressures must be ABSOLUTE pressures. Because the top of the manometer is exposed to the background air rather than a vacuum, the pressures in units of mmHg are gauge pressures, not absolute pressures.
It doesn't matter what units you eventually use for pressure, as long as they are the same, and as long as you use absolute pressure.

How to get absolute pressure from gauge pressure:
P_abs = Pbg + Pgauge

Thus:
P1 = Pbg + P1g
P2 = Pbg + P2g

Substitute:
T2 = T1*(Pbg + P2g)/(Pbg + P1g)

Data:
T1:=273.15 K; Pbg:=760 mmHg; P1g:=120 mmHg; P2g:=30 mmHg;

Results:
T2 = 245.2 Kelvin, which translates to T2 = -27.9 Celsius