Question

Calculate the work done when two moles of an ideal gas expand isothermally from 5 atmosphere pressure to 2 atmospheric pressure at 50 C. What is the amount of heat absorbed

Answer 1

Given info : two moles of an ideal gas expand isothermally from 5atm to 2atm at 50°C

To find : the workdone on the gas and the heat absorbed by gas.

Solution : as gas expands isothermally, change in internal energy must be zero. so, Q = W

i.e., heat absorbed must be equal to work done on the gas.

W = ∫PdV

We know, PV = nRT

P = nRT/V

so, W = nRT∫dV/V = nRT ln[V₂/V₁]

From Boyle's law, P₁V₁ = P₂V₂

so, V₂/V₁ = P₁/P₂

then, W = nRT ln[P₁/P₂]

Now using values of terms.

= 2 × 25/3 × (273 + 50) ln(5/2)

= 50/3 × 323 ln(2.5)

= 6216.67 ln(2.5)

= 5696.2771 J

= 5.696 ≈ 5.7 kJ

Therefore workdone or heat absorbed by the gas is 5.7 kJ