Ideal Gas Equation from KTG

Q.

A vessel of volume $V$ contains an ideal gas at absolute temperature $T$ and pressure $P$. The gas is allowed to leak till its pressure falls to $P$. Assuming that the temperature remains constant during leakage, the number of moles of the gas that have leaked is

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 200${}^{\circ }$C. During the day the temperature rises to 400${}^{\circ }$C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature

1. 355 kPa

2. 392 kPa

3. 209 kPa

4. 285 kPa

Q. A cylinder of fixed capacity 44.8 litre. contains a monatomic gas at standard temperature and pressure. The amount of heat required to increse the temperature of cylinder by ${10}^{\circ }$C will be. (R = universal gas constant)

1. R
2. 10R
3. 20R
4. 30R

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.

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. P

2. 8P

3. 2P

4. P/8

Q. PV=nRT is exactly true for all gases under all conditions.

1. False
2. True

Q.

Boyle's, Charles' and Avogadro's results on the different state variables of a gas, can be combined into one "equation of state” known as the ideal gas equation, PV = nRT, where R = 8.514 J/mol-K. Consider the following situation.

A mixture of hydrogen and oxygen has volume $2000c{m}^3$, temperature 300 K, pressure 100 kPa and mass 0.76 gms. Calculate the masses of hydrogen and oxygen in the mixture.

1. 0.12 gms; 0.64 gms

2. 0.8gms; 0.68 gms

3. 0.24 gms; 0.52 gms

4. 0.16gms; 0.60 gms

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

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. A vessel of volume $8.0\times {10}^{-3}{m}^3$ contains an ideal gas at 300k and 200k Pa. The gas is allowed to leak till the pressure falls to 125 k Pa. Calculate the amount of gas (in moles) leaked assuming that the temperature remains constant.

1. 0.24 moles
2. 0.54 moles
3. 0.34 moles
4. 0.44 moles