Gas Pressure and Temperature

Q.

The ideal gas law, which relates the P, V and temperature T of an ideal gas in a closed box, given as PV = nRT, can be manipulated to construct an effective thermometer. A "constant volume gas thermometer” uses a sample of gas (commonly, nitrogen or helium) in a closed chamber, thus fixing the volume V. The temperature is then measured by reading off the corresponding pressure P. At the freezing point of water, it is seen that a gas thermometer records a pressure of 0.9 x 10⁵ Pa; it also records a pressure of 1.2 x 10⁵ Pa at the boiling point of water. What pressure will you find in the gas chamber at a room temperature of 23⁰C?

1. 0.81 x 10⁵ Pa

2. 1.34 x 10⁵ Pa

3. 0.64 x 10⁵ Pa

4. 0.97 x 10⁵ Pa.

Q.

You might be familiar with the ideal gas equation from Chemistry, which relates the pressure and volume of an ideal gas with temperature as: $PV$ = $nRT$, where $nR$ is a constant. You are given a closed metal container of volume $V$, filled with a gas kept at a temperature $T$, and pressure $P$. If $\gamma$ is the coefficient of volume expansion for the gas, what is the pressure after the temperature is increased by $\Delta T$?

1. $P^{\prime }$ = $P(1+\gamma \Delta T)$

2. $P^{\prime }$ = $P(1-\gamma \Delta T)$

3. $P^{\prime }$ = $P$

4. $P^{\prime }$ = $\frac{P}{(1+\gamma \Delta T)}$

Q.

Before we tackle a constant volume situation for an ideal gas let us think about an equivalent problem, where we keep the pressure constant, while volume is allowed to increase. If $\gamma$ is the coefficient of volume expansion at a temperature $T$, which of the following is true?

1. $\gamma$ is more or less constant, and independent of $T$.

2. Insufficient data. Need to know the final temperature

3. $\gamma$ = $T^{-1}$

4. $\gamma$ = $\frac{1}{T^2}$

Q.

In a constant volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a U-tube connected to the gas at one end. When the bulb is placed at the room temperature 27.0℃, the mercury column in the arm open to atmosphere stands 5.00 cms above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes 45.0 cms. Calculate the temperature of the liquid. (Atmospheric pressure = 75.0 cm of mercury.)

1. 155℃

2. 177℃

3. 187℃

4. 165℃.