Ideal Gas Law

Q.

Two glass bulbs A and B are connected by very small tube having a stop cock. Bulb A has a volume of 100 ml and contained the gas while bulb B was empty and has a volume of 150 ml. On opening the stop cock, the pressure of the gas in bulb A will fall down to___.

1. 80%

2. 60%

3. 40%

4. 20%

Q. Two Cylinders $A$ and $B$ of equal capacity are connected to each other via a stop cock. $A$ contains an ideal gas at standard temperature and pressure, $B$ is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened.The process is

1. $\text{Isochoric}$
2. $\text{Isobaric}$
3. $\text{Isothermal}$
4. $\text{Adiabatic}$

Q. A monoatomic ideal gas is used in a carnot engine as the working substance. If during the adiabatic compression the volume of the gas decreases from v to $\frac{v}{8}$, the efficiency of the engine is

1. 0.5
2. 0.25
3. 0.75
4. 0.4

Q. Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure?
Where, $1\to 2$ is adiabatic.
(Graphs are schematic and are not to scale)

1. 
2. 
3. 
4. 

Q. One mole of a monoatomic ideal gas is taken through the cycle shown in figure.
$A\to B:$ Adiabatic expansion
$B\to C:$ Cooling at constant volume
$C\to D:$ Adiabatic compression.
$D\to A:$ Heating at constant volume
The pressure and temperature at $A,B,C$ and $D$ are denoted by $(P_A,T_A),(P_B,T_B),(P_C,T_C)$ and $(P_D,T_D)$ respectively. Given $T_A=1000\text{K},P_B=\frac{2}{3}{P}_A$ and $P_C=\frac{1}{3}{P}_A$, the work done by the gas in the process $A\to B$ is


[Take $R=8.31\text{J/mol K}$]

1. $1869.75\text{J}$
2. $970.23\text{J}$
3. $1123\text{J}$
4. $875.32\text{J}$

Q. One mole of a monoatomic ideal gas undergoes a cyclic process as shown in the figure (where, $V$ is the volume and $T$ is the temperature ). Which of the statement(s) given below is (are) true?

1. Process $\text{I}$ is an isochoric process
2. In process $\text{II}$, gas absorbs heat
3. In process $\text{IV}$, gas release heat
4. Process $\text{I}$ and $\text{II}$ are not isobaric

Q. Match List-I with List-II.

List-I	List-II
$\left(a\right)$ Isothermal	$\left(i\right)$ Pressure constant
$\left(b\right)$ Isochoric	$\left(ii\right)$ Temperature constant
$\left(c\right)$ Adiabatic	$\left(iii\right)$ Volume constant
$\left(d\right)$ Isobaric	$\left(iv\right)$ Heat content is constant

Choose the correct answer from the options given below -

1. $\left(a\right)-\left(ii\right),\left(b\right)-\left(iv\right),\left(c\right)-\left(iii\right),\left(d\right)-\left(i\right)$
2. $\left(a\right)-\left(ii\right),\left(b\right)-\left(iii\right),\left(c\right)-\left(iv\right),\left(d\right)-\left(i\right)$
3. $\left(a\right)-\left(i\right),\left(b\right)-\left(iii\right),\left(c\right)-\left(ii\right),\left(d\right)-\left(iv\right)$
4. $\left(a\right)-\left(iii\right),\left(b\right)-\left(ii\right),\left(c\right)-\left(i\right),\left(d\right)-\left(iv\right)$

Q. A loop of $6.28cm$ long thread is put gently on a soap film in a wire loop. The film is pricked with a needle inside the soap film enclosed by the thread. If the surface tension of soap solution is $0.030N/m$, then the tension in the thread is

1. $1\times {10}^{-4}N$
2. $2\times {10}^{-4}N$
3. $3\times {10}^{-4}N$
4. $4\times {10}^{-4}N$

Q. For an adiabatic compression, (for an ideal gas) the quantity $\frac{T}{V}$(where $T$ = temperature and $V$ = volume)

1. decreases
2. increases
3. depends on atomicity of gas
4. remains constant

Q. One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?

1. Process I is an isochoric process
2. In process II, gas absorbs heat
3. In process IV, gas releases heat
4. Processes I and II are not isobaric

Q. The length of a wire is $4m$. Its length is increased by $2mm$ when a force acts on it. The strain is:

1. 0.5 x 10${}^{-3}$
2. 5 x 10${}^{-3}$
3. 2 x 10${}^{-3}$
4. 0.05

Q. At 11 atm and ${27}^{o}C$ volume of a balloon filled with a gas is 500 ml. The stretching capacity of the balloon is 33 times the volume of the gas at $1$atm.The temperature above which the balloon bursts is:

1. ${900}^{o}C$
2. ${627}^{o}C$
3. ${300}^{o}C$
4. $627K$

Q. Find the maximum load which may be placed on a tungsten wire of diameter $2mm$ so that permitted strain must not exceed $\frac{1}{1000}$.
$(Y_{tungsten}=35\times {10}^{10})$

1. $4000N$
2. $1100N$
3. $200N$
4. $300N$

Q. Review. A steel wire and a copper wire, each of diameter 2.000 mm, are joined end to end. At ${40.0}^{0}C$, each has an unstretched length of 2.000 m. The wires are connected between two fixed supports 4.000 m apart on a tabletop. The steel wire extends from $x=-2.000m$ to $x=0$, the copper wire extends from $x=0$ to $x=2.000m$, and the tension is negligible. The temperature is then lowered to ${20.0}^{0}C$. Assume the average coefficient of linear expansion of steel is $11.0\times {10}^{-6}{(}^{0}C{)}^{-1}$ and that of copper is $17.0\times {10}^{-6}{(}^{0}C{)}^{-1}$. Take Young’s modulus for steel to be $20.0\times {10}^{10}N/m^2$ and that for copper to be $11.0\times {10}^{10}N/m^2$. At this lower temperature, find (a) the tension in the wire and (b) the x coordinate of the junction between the wires.