Question

Two moles of helium gas initially at 195 K and 0.32 atm are compressed isothermally to 1.83 atm.

a) Find the final volume of the gas. Assume that helium behaves as an ideal gas. The universal gas constant is 8.31451 J/K

Answer 1

A) Ideal gas law:
P2*V2 = n*R*T

1.83 atm = 185.42 kPa

0.32 atm = 32.4 kPa

Solve for V2:
V2 = n*R*T/P2

V2 = 17.487 litres = 17.487 * 10^-3 m^3

Similarly, we will be interested in V1:
V1 = n*R*T/P1

V1 = 100.07 litres = 100.07 * 10^-3 m^3

T is the same for both state 1 and state 2, because of what the word "isothermally" means.

B) Formula for work done by an ideal gas in a reversible isothermal expansion. This is an isothermal compression, so it will come out negative indicating work is done on the gas.

W = P1*V1*ln(V2/V1)

With substitutions:
W = n*R*T*ln(P1/P2)

W = -5457.467 J = -5.45 kJ

C) First law of Thermodynamics:
Q = deltaU + W

For the isothermal process, no change in temperature. For an ideal gas, internal energy is exclusively a function of temperature, flavor and amount of gas. Thus, deltaU=0 for isothermal processes.

So, Q=W, which means
Q = n*R*T*ln(P1/P2)

Q = -5.45 kJ