Determine the amount of work (in J) done on an ideal gas as it is heated in an enclosed, thermally isolated cylinder topped with a freely moving piston. The cylinder contains 0.180 mol of the gas and the temperature is raised from 21.0°C to 250°C. The piston has a mass of 8,500 g and an area of 5.50 cm2.

W = - 342.70 J

Explanation:

Given:

The mass of the piston, m = 8500 g

Area of the piston, A = 5.50 cm²

initial temperature of the gas, T₁ = 21.0° C = 294 K

Final temperature of the gas, T₂ = 250° C = 523 K

Moles of gas present, n = 0.180 mol

now,

we know

PV = nRT

or

V = nRT/P

where,

P is the pressure

R is the gas constant = 8.314 J / mol. K

V is the volume

Now,

for the initial stage

V₁ = nRT₁/P

and for the final stage

V₂ = nRT₂/P

now, the change in volume is

ΔV = V₂ - V₁

or

ΔV = (nRT₂/P) - (nRT₁/P)

or

ΔV = (1/P) (nR) (T₂ - T₁)

now,

the work done (W) is given as:

W = PΔV

since the work is on the gas, thus

W = - PΔV

on substituting the values, we get

W = - P (1/P) (nR) (T₂ - T₁)

or

W = - (nR) (T₂ - T₁)

on substituting the values in the above equation, we get

W = - (0.180 * 8.314) (523 - 294)

or

W = - 342.70 J