Gas Laws

Step 1: Given γ = 1
Step 2: PV = constant
Step 3: This is the condition for an isothermal process.

Step 1: Isothermal expansion definition.
In an isothermal process, the temperature of the gas remains constant. The relationship between pressure and volume during an isothermal expansion is governed by .

Step 2: Deriving the expression.
The differential change in pressure is related to the change in volume by: Thus, the correct answer is (2).

Step 1: Use the combined gas law.
Since the temperature remains constant, we apply Boyle's Law for each gas: Using the given pressures and volumes for each container, we find the total pressure after the gases mix.
Step 2: Calculate the final pressure.
The final pressure is found to be 0.98 MPa. Final Answer:

Step 1: Use the ideal gas law.
Using the ideal gas law , the pressure is proportional to the number of moles and the temperature. The pressure in the He vessel will be twice the pressure in the vessel due to the temperature doubling.
Step 2: Conclusion.
The pressure in the He vessel will be . Final Answer:

Step 1: From ideal gas equation:
Step 2: Since and are same for both balloons, number density is the same.

Step 1: For adiabatic process: TV^γ-1 = constant
Step 2: 300 × 2^γ-1 = 200 × VD^γ-1
Step 3: Solving gives VD < 4.

Step 1: Recall Graham's law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass: where is the molar mass of the gas.
Step 2: Compare the molar masses of the given gases:
- O : ,
- CO : ,
- H : ,
- N : .
Step 3: Determine the gas with the lowest molar mass.
H has the smallest molar mass (2 g/mol), so it will have the highest rate of diffusion.