Ideal Gas Equation from KTG

Q.

The root mean square (R.M.S.) Speed V of the molecules of an ideal gas is given by the expressions,

v = √ (3RT/M) and

v = √ (3KT/m) where R is universal gas constant, T is the absolute (Kelvin) temperature M is the molar mass, K is Boltzman's constant and M is the molecular mass. The R.M.S. speed of oxygen molecules (O₂) at temperature T₁ is V₁. When the temperature is doubled, if the oxygen molecules are dissociated into atomic oxygen, what will be R.M.S. speed of oxygen atoms? (Treat the gas as ideal).

1. v₁/2

2. v₁

3. 2v₁

4. 

Q.

One mole of ideal gas follows a law according to that it's pressure varies with volume as p= $\frac{a}{1+\frac{v}{b}}$where a and b are positive constant the temperature of the gas at volume v= a is

Q. An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J mol¯¹ K¯, molecular mass of O2 = 32 u).

Q.

A vessel contains $1$ mole of $O_2$ gas (molar mass $32$) at a temperature $T$. The pressure of the gas is $P$. An identical vessel containing one mole of $He$ gas (molar mass $4$) at a temperature $2T$ has a pressure of

1. $\frac{P}{8}$

2. P

3. 2P

4. 8P

Q. Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP : 1 atmospheric pressure, 0 °C). Show that it is 22.4 litres.

Q. Figure 13.8 shows plot of PV/T versus P for 1.00×10–3 kg of oxygen gas at two different temperatures . (a) What does the dotted plot signify? (b) Which is true: T1 > T2 or T1 < T2? (c) What is the value of PV/T where the curves meet on the y-axis? (d) If we obtained similar plots for 1.00×10–3 kg of hydrogen, would we get the same value of PV/T at the point where the curves meet on the y-axis? If not, what mass of hydrogen yields the same value of PV/T (for low pressure high temperature region of the plot) ? (Molecular mass of H₂ = 2.02 u, of O₂ = 32.0 u, R = 8.31 J mo1¯¹ K¯¹.)

Q.

4 moles of an ideal gas is at $0^{\circ }C$. At constant pressure it is heated to double its volume, then its final temperature will be

1. 0°C

2. 273°C

3. 546°C

4. 136.5°C

Q.

A long cylindrical tank of cross-section area 0.5$m^2$ is filled with water. It has an opening at a height 50 cm from the bottom, having area of cross-section $1\times {10}^{-4}{m}^2$ . A movable piston of cross-section area almost equal to 0.5 $m^2$ is fitted on the top of the tank such that it can slide in the tank freely. A load of 20 kg is applied on the top of the water by piston, as shown in the figure. Find the speed of the water jet with which it hits the surface when piston is 1m above the bottom (Ignore the mass of the piston).

1. 3.56 m/s

2. 3.3 m/s

3. 5.56 m/s

4. 4.56 m/s

Q. 35. Calculate the rms speed of an ideal monatomic gas having molecular weight 28 gm/mol at 27 CIf the specific heats at constant pressure and volume are respectively 20.8 J mol-1 K-1 and12.5 J mol-1 K-1 respectively.

Q. RMS speed of molecules of gas A at temperature T1 is v and that of molecules of gas B at temperature T2 is 2v. Then which of the following is necessarily true? Options: 1)T2 = 2T1 2)T2 < T1 3)T2 > T1 4)None of these

Q. 10.A closed vessel 0.2m3 contains hydrogen gas at 300k and pressure 10`5pa. Then heat required to raise the temperature to 600 k is. What is the formula to find the heat?.

Q. The factor $\frac{R}{N_A}$ in an ideal gas law is

1. Celsius constant
2. Characteristic gas constant
3. Universal gas constant
4. Boltzmann’s constant

Q.

A quantity of air is taken from state a to state b along a path that is a straight line in the P-V diagram.In this process, what happens to the temperature of the gas?

1. Decreases

2. Remains constant

3. Not enough information

4. Increases

Q. 8. The temperature (T) of one mole of an ideal gas varies with its volume (V) aswT=-alpha V3 +beta V2 where alpha and beta are positive constants. The maximum pressure of gas during this process is ?

Q. A gas has a density of $3\text{g/L}$ at S.T.P. What is its molar mass?

1. $67.2\text{g}$
2. $40\text{g}$
3. $20.4\text{g}$
4. $10\text{g}$

Q. 22.When two moles of ideal gas ( Cp =5/2R ) heated from 300K to 600K at constant pressure, the Δ S is ________

Q.

Two thermally insulated vessels $1$ and $2$ are filled with air at temperature ($T_1$, $T_2$), volume ($V_1$, $V_2$) and pressure ($P_1$, $P_2$) respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

1. T₁ +T₂

2. (T₁ + T₂)/2

3. T₁T₂(P₁V₁+P₂V₂)/P₁V₁T₂+P₂V₂T₁)

4. T₁T₂(P₁V₁+P₂V₂)/P₁VT₁+P₂V₂T₂)

Q. electric metre cylinder of Oxygen gas at 4 ATM pressure and 17°C colleagues developed when the league was repaired 2.5 ATM pressure of Oxygen gas remained in the cylinder, still at27°C.how many moles of gas escaped?

Q. Calculate the rms speed of an ideal monoatomic gas having molecular weight 28gm/mol at 27°C. If the specific heats at constant pressure and volume are respectively 6.3J/mol K and 3.14J/mol K respectively.

Q. An ideal gas is expanding such that $PT=$ constant. The coefficient of volume expansion of the gas is :

1. $\frac{1}{T}$
2. $\frac{2}{T}$
3. $\frac{3}{T}$
4. $\frac{4}{T}$

Q. The volume of containers A and B, connected by a tube and a closed valve are $V$ and $4V$ respectively. Both the containers A and B have the same ideal gas, at pressures $5.0\times {10}^5\text{Pa}$ and $1.0\times {10}^5\text{Pa}$ and temperatures $300\text{K}$ and $400\text{K}$ respectively. The valve is opened to allow the pressure to equalise, but the temperature of each container is kept constant at its initial value. Find the common pressure in the containers.

1. $2.5\times {10}^5\text{Pa}$
2. $2.0\times {10}^5\text{Pa}$
3. $3.0\times {10}^5\text{Pa}$
4. $1.5\times {10}^5\text{Pa}$

Q. A mixture of ideal gases has 2 moles of He, 4 moles of oxygen and 1 mole of ozone at absolutetemperature T. The internal energy of mixture is(1) 13 RT(3) 16 RT(2) 11 RT(4) 14 RT

Q. 39.calculate the rms speed of an ideal diatomic gas having molecular weight 32 gm/mol at 0 degree c. if the specific heats at constant pressure and volume are respectively 8.3 j/mol k and 6.34 cal/mol k respectively.

Q.

Two thermally insulated vessels $1$ and $2$ are filled with air at temperature ($T_1$, $T_2$), volume ($V_1$, $V_2$) and pressure ($P_1$, $P_2$) respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

1. $T_1+T_2$

2. $\frac{T_1+T_2}{2}$

3. $\frac{T_1{T}_2(P_1{V}_1+P_2{V}_2)}{P_1{V}_1{T}_2+P_2{V}_2{T}_1)}$

4. $\frac{T_1{T}_2(P_1{V}_1+P_2{V}_2)}{P_1{V}_1{T}_1+P_2{V}_2{T}_2)}$

Q.

An enclosure of volume $V$ contains a mixture of $8g$ of oxygen, $14g$ of nitrogen and $22g$ of carbon- dioxide at absolute temperature $T$. The pressure of the mixture of gases is ($R$ is universal gas constant)

1. 

2. 

3. 

4. 

Q.

Air is pumped into an automobile tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is 200C. During the day the temperature rises to 400C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature

1. 209 kPa

2. 285 kPa

3. 355 kPa

4. 392 kPa

Q. How many moles of $O_2$ gas are present in a sample which occupies a volume of 1.50 litres at 5.00 atmospheres pressure and ${70}^{o}C$ temperature?

1. 0.266
2. 0.536
3. 0.036
4. 0.103

Q. The factor $\frac{R}{N_A}$ in an ideal gas law is

1. Celsius constant
2. Characteristic gas constant
3. Universal gas constant
4. Boltzmann’s constant

Q. A vessel of volume $2000c{m}^3$ contains 0.1 mole of $O_2$ and 0.2 mole of $C{O}_2$. If the temperature of the mixture is 300k, find its pressure.

1. $1.25\times {10}^{5}Pa$
2. $2.25\times {10}^{5}Pa$
3. $3.25\times {10}^{5}Pa$
4. $4.25\times {10}^{5}Pa$

Q.

The relation between volume $V$ pressure $P$ and absolute temperature $T$ of an ideal gas is $PV=xT$ where x is a constant. The value of x depends upon

1. The mass of the gas molecule

2. The average kinetic energy of the gas molecules

3. P, V and T

4. The number of gas molecules in volume V