Question

2. A cylinder is filled with helium gas at 323 K and 118 atmospheres. The volume of the cylinder is 3.07 liters. What is the total number of atoms in the gas?

3. One mole of helium gas at 297 K is allowed to expand slowly (isothermally) from an initial volume of 3.50 liters to a final volume of 16.1 liters. How much heat flows into the gas?

4. Helium gas is kept in a container surrounded by perfect vacuum p=0 (e.g. in space). The pressure inside the container is 288 Pa. Suddenly, the container breaks and the gas expands rapidly (i.e. adiabatically). What is the pressure of the gas when the volume has tripled?

Answer 1

PART 2:

Use ideal gas equation to find no.of moles of gas (n):

Therefore, No.of atoms is given by:

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PART 3:

According to First law of thermodynamics, Heat supplied to a system (Q) will be used to do work (W) and to rise internal energy (U):

That is:

Here, process is isothermal (temperature constant). Hence, change in internal energy will be zero.

That is Heat flown into the gas is given by:

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PART 4:

For an adiabatic process, we have:

Let V be the initial volume. Hence final volume will be 3V.

For monatomic gases like helium,

Substituting in equation:

Hence, Final pressure (P₂) is given by: