A cylinder with a movable piston holds 2.75 mol of argon gas at a constant

temperature of 295 K. As the gas is compressed isothermally, its pressure increases from
101 kPa to 121 kPa. Find (a) the final volume of the gas, (b) the work done by the gas,
and (c) the heat added to the gas.

(a) PV = constant for an isothermal gas

(b) Work done = -Integral of P dV
= -integral of PoVo*dV/V
= PoVo*dP/P
= PoVo ln(P2/P1)

(c) Qin = Wout + deltaU
= Wout

The internal energy does not change for an ideal isothermal gas.

To find the final volume of the gas, we can use Boyle's law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.

Boyle's Law formula:
P1V1 = P2V2

Given:
P1 = 101 kPa (initial pressure)
P2 = 121 kPa (final pressure)
V1 = Initial volume (unknown)
V2 = Final volume (unknown)

Using the formula, we can rearrange it to solve for V2:
V2 = (P1 * V1) / P2

To find the work done by the gas, we can use the formula:
Work (W) = -P * ΔV

Where:
P = average pressure
ΔV = change in volume (V2 - V1)

To find the heat added to the gas, we can use the first law of thermodynamics:
ΔU = Q - W

Where:
ΔU = change in internal energy
Q = heat added to the gas (unknown)
W = work done by the gas

Now, let's plug in the given values and solve for the unknowns:

(a) Final volume of the gas (V2):
V2 = (P1 * V1) / P2

(b) Work done by the gas (W):
W = -P * ΔV
W = -(average pressure)*(final volume - initial volume)

(c) Heat added to the gas (Q):
Q = ΔU + W

To calculate ΔU, we need to know if the process is reversible or irreversible and its molar specific heat capacity.

Note: Additional information about the process is required to calculate ΔU and Q.