300 milimole of perfect gas occupies 13 lit at 320 k ,calculate the work done in joule ,when the gasexpands

A)isothermally against a constant pressure of .20 atm
Isothermal and reversible process
c)Into vaccum until volume of gas is increased by 3 ltr

Note: L is liter.

K is kelvin.

165 joule

i.60.79

ii.165.
iii.0

To calculate the work done by a gas during expansion, we need to use the equation:

Work = -Pext * ΔV

where Pext is the external pressure and ΔV is the change in volume.

Let's calculate the work done in each scenario:

A) Isothermal Expansion against constant pressure:

Given:
Initial volume (Vi) = 13 L
Final volume (Vf) = Vi + ΔV (unknown)
Pressure (P) = 0.20 atm
Temperature (T) = 320 K

First, we need to calculate the value of ΔV:
ΔV = Vf - Vi

Now, since it's an isothermal process, the ideal gas law can be used to relate pressure, volume, and temperature:

PV = nRT

Rearranging the equation to solve for V:
V = (nRT) / P

Substituting the given values:
Vi = (300 mmol * 0.0821 L·atm/mol·K * 320 K) / 0.20 atm

Now, we can calculate the final volume (Vf) by adding the change in volume (ΔV) to the initial volume (Vi):
Vf = Vi + ΔV

Finally, we can calculate the work done (W) using the equation mentioned earlier:
W = -Pext * ΔV

Substituting the given values of Pext and ΔV, calculate W in joules.

B) Isothermal and Reversible Process:

If the process is both isothermal and reversible, the work done can be calculated using the equation:

Work = -nRT * ln(Vf / Vi)

Using the same values of n, R, T, Vi, and Vf from the first scenario, substitute them into the equation to calculate the work done (W) in joules.

C) Expansion into vacuum:

Given:
Initial volume (Vi) = 13 L
Final volume (Vf) = Vi + ΔV (Vi + 3 L)
Pressure (P) = 0 atm (vacuum)

Since the pressure is zero (vacuum), the work done will also be zero. In a vacuum, there is no external pressure acting on the system, so no work is done during the expansion.

Note: It's important to convert all units to a consistent system, such as liters and atmospheres, to ensure accurate calculations. Also, double-check all unit conversions and ensure that the gas constant (R) is in the appropriate units for the desired calculation.