Gas Pressure and Temperature

Q.

A thermodynamic cycle $xyzx$ is shown on a $V-T$ diagram .

The$P-V$ diagram that best describes this cycle is : (Diagrams are schematic and not upto scale)

1. 

2. 

3. 

4. 

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. 0.64 x 10⁵ Pa

2. 0.81 x 10⁵ Pa

3. 1.34 x 10⁵ Pa

4. 0.97 x 10⁵ Pa.

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. Insufficient data. Need to know the final temperature

2. is more or less constant, and independent of .

3. =

4. =

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. 177℃

2. 155℃.

3. 155℃

4. 177℃

Q. The pressure of air in the bulb of a constant volume gas thermometer at $0^{\circ }$C and ${100}^{\circ }$C are 73.00 cm and 100 cm of mercury respectively. Calculate the pressure at room temperature ${20}^{\circ }$C.

1. $88.4cm$ of Hg
2. $98.4cm$ of Hg
3. $108.4cm$ of Hg
4. $78.4cm$ of Hg

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' = P

2. P' = P (1 + γ∆T)

3. P' = P (1 - γ∆T)

4. P' = P/(1 + γ∆T)