Gas Pressure and Temperature

Q. A scientist says that the efficiency of his heat engine which works at source temperature ${127}^{\circ }\text{C}$ and sink temperature ${27}^{\circ }\text{C}$ is $26\%$, then

1. It is possible but less probable
2. Data are incomplete
3. It is quite probable
4. It is impossible

Q. The volumes of two vessels are $5\text{litre}$ and $3\text{litre}$ respectively. Air is filled in them at pressure of $3$ atm and $5$ atm respectively. At constant temperature if they are connected through a tube, the resultant pressure will be

1. $4.25\text{atm}$
2. $4\text{atm}$
3. $3.75\text{atm}$
4. $3.5\text{atm}$

Q. A heat engine is involved with exchange of heat of $1915J,-40J,+125J\text{and}-QJ$, during one cycle achieving an efficiency of $50.0$%. The value of $Q$ is

1. $640\text{J}$
2. $40\text{J}$
3. $980\text{J}$
4. $400\text{J}$

Q. A reversible heat engine converts one-fourth of the input into work. When the temperature of the sink is reduced by $52\text{K}$, its efficiency is doubled. The temperature in Kelvin of the source will be

Q.

The pressure of the gas in a constant volume gas thermometer is 70 kPa at the ice point. Find the pressure at the steam point.

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

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. 177℃

3. 155℃.

4. 155℃

Q. One reversible heat engine operates between $900\text{K}$ and $T_2\text{K}$, and another reversible heat engine operates between $T_2\text{K}$ and $400\text{K}$. If both the engine have the same efficiency, then the temperature $T_2$ must be equal to

1. ${600}^{\circ }\text{C}$
2. $300\text{K}$
3. $600\text{K}$
4. $650\text{K}$

Q. One mole of an ideal gas undergoes a process, whose process equation is given as $P=\frac{P_0}{1+{\left(\frac{V_0}{V}\right)}^2}$ Here $P_0$ and $V_0$ are constants. When the volume of the gas is changed from $V_0$ to $3V_0,$ find the change in the temperature of the gas.

1. $\frac{7P_0{V}_0}{2R}$
2. $\frac{11P_0{V}_0}{5R}$
3. $\frac{7P_0{V}_0}{R}$
4. $\frac{11P_0{V}_0}{R}$

Q. A Carnot engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is reduced by ${62}^{\circ }\text{C}$, its efficiency is doubled. The temperatures of the source and the sink are respectively

1. ${62}^{\circ }\text{C},{124}^{\circ }\text{C}$
2. ${99}^{\circ }\text{C},{37}^{\circ }\text{C}$
3. ${124}^{\circ }\text{C},{62}^{\circ }\text{C}$
4. ${37}^{\circ }\text{C},{99}^{\circ }\text{C}$

Q.

Two ideal gas thermometers Aand Buse oxygen and hydrogen respectively. The following observations are made:

Temperature	Pressure thermometer A	Pressure thermometer B
Triple-point of water	1.250 × 105 Pa	0.200 × 105 Pa
Normal melting point of sulphur	1.797 × 105 Pa	0.287 × 105 Pa

(a) What is the absolute temperature of normal melting point of sulphur as read by thermometers Aand B?

(b) What do you think is the reason behind the slight difference in answers of thermometers Aand B? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?

Q.

Two ideal gas thermometers Aand Buse oxygen and hydrogen respectively. The following observations are made:

Temperature Pressure Pressure

thermometer A thermometer B

Triple-point of water 1.250 × 10⁵ Pa 0.200 × 10⁵ Pa

Normal melting point 1.797 × 10⁵ Pa 0.287 × 10⁵ Pa

of sulphur

(a) What is the absolute temperature of normal melting point of sulphur as read by thermometers Aand B?

(b) What do you think is the reason behind the slight difference in answers of thermometers Aand B? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?

Q. A barometer kept in an elevator reads $76cm$ when the elevator is accelerating upwards. The most likely pressure inside the elevator (in $cm$ of $Hg$) is

1. $76$
2. $77$
3. $75$
4. $74$

Q. An engine has an efficiency of $1/6$. When the temperature of sink is reduced by ${62}^{\circ }C$, its efficiency is doubled. The temperature of source will be

1. ${62}^{\circ }C$
2. ${37}^{\circ }C$
3. ${99}^{\circ }C$
4. ${124}^{\circ }C$

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

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 the given figure, ${\rho }_1,{\rho }_2$ density of liquid in container (1) & (2), and ${\rho }_3$ density of liquid (2) of manometer The level of fluid in both the container is same. Which is the correct condition?

1. ${\rho }_2>{\rho }_1$
2. ${\rho }_2={\rho }_1$
3. ${\rho }_2<{\rho }_1$
4. cant say

Q. A uniform meter scale of mass is suspended by two vertical strings attached to its two ends. a body of mass 2m is placed on 75 cm mark. the tension in the two strings are in the ratio

1. 1:2
2. 1:3
3. 1:4
4. 3:4

Q. The pressure measured by a constant volume gas thermometer is $40kPa$ at the triple point of water. What will be the pressure measured at the boiling point of water (${100}^{0}C$)?

Q. A given quantity of an ideal gas is at pressure P and absolute temperature T. The isothermal bilk modulus of the gas is?

1. $2P/3$
2. P
3. $3P/2$
4. $2P$

Q. Constant volume gas thermometer works on:

1. Boyle's Law
2. Gay-Lussac's Law
3. Charle's Law
4. All of the above

Q. The coefficient of volume expansion of liquid is $\gamma$. The fractional change in its density for $\Delta T$ rise in temperature is :

1. $\gamma \Delta T$
2. $1+\gamma \Delta T$
3. $\frac{\Delta T}{\gamma }$
4. $1-\gamma \Delta T$

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. A vertical hollow cylinder of height $1.52m$ is fitted with a movable piston of negligible mass and thickness. The lower half of the cylinder contains an ideal gas and the upper half is filled with mercury. The cylinder initially at $300K$. When the temperature is raised half of the mercury comes out of the cylinder. Find the temperature assuming the thermal expansion of mercury to be negligible.

Q. A uniform cord of length $25cm$ and mass $15g$ is initially stuck to a ceiling. Later, it hangs vertically from the ceiling with only one end still stuck. What is the change in the gravitational potential energy of the cord with this change in orientation? (Hint: Consider a differential slice of the cord and then use integral calculus.)

Q. A gaseous mixture enclosed in a vessel of volume V consists of one mole of a gas A with $\gamma$ = $\frac{5}{3}$ and another gas B with $\gamma$ = $\frac{7}{5}$ at a certain temperature T. the molar masses of the gases A and B are 4 and 32, respectively. The gases A and B do not reach with each other and are assumed to be ideal. The gaseous mixture follows the equation P$V^{\frac{19}{13}}$ = constant, in adiabatic processes. The number of moles of the gas B in the gaseous mixture.

1. 3
2. 4
3. 5
4. 2