Question

How do you do this? How do you set it up?

One mole of a ideal gas initially at temp To=0C undergoes an expansion at a constant pressure of 1atm to four times it original volume. (a) calculate the new temp Tf of the gas. (b) calulate the wok done by the gas during the expansion.

Answer 1

Given :

Initial temperature, T₀ = 0'C = 0+273 = 273 K

Pressure, P = 1 atm = 101325 Pa

Let the initial volume, V_i = V

Final volume, V_f = 4*V_i = 4*V

Number of moles, n = 1

Since the gas is ideal, we can use the ideal gas equation : PV = n*R*T

Since P is kept constant, n and R are already constant, thus we get : V/T = constant.

Thus, the ratio of V/T remains constant, even when the variables are changed individually. This is also known as Charles' law, and can be stated as : V_i/T_i = V_f/T_f

where the subscripts 'i' and 'f' denote initial and final conditions respectively.

Putting values, V_i = V, V_f = 4*V, T_i = T₀ = 273 K , we get

(a) T_f = V_f*T_i/V_i = 4*V*273/V = 1092 K

Work done by the gas, W = =

P.( V_f-V_i ) = 101325*(4*V - V ) = 3*V*101325

Note : While integrating, we keep P constant. Hence it is taken out of the integral while integration.

From the ideal gas law, we know, V = n*R*T/P

So, W = 3*101325*n*R*T/ P = 3*101325*8.314*273/101325 = 6809.16 Joules = 6.809 kJ