Question

A cylinder contains 4 m3 of ideal gas at a pressure of 1 bar. This gas is compressed in a quasi-equilibrium isothermal process till its pressure increases to 4 bar. The work in kJ required for this process is

Answer 1

any reversible process is known as quassi-static process.
here the cylinder contains 4m³ of ideal gas at pressure 1bar . the gas is now compressed in quassi-static equilibrium isothermal process till the pressure increases to 4bar.

so, work done is given as $W=-P_1V_1ln\frac{P_2}{P_1}$

Here, $P_1=1bar=10^5Pa$
$P_2=4bar=4\times10^5Pa$
$V_1=4m^3$

so, W = 10^5 × 4 ln{1 × 10^5/4 × 10^5} Joule
= 4 × 10^5 ln(1/4) Joule
= -4 × 10^5 × 2ln2 Joule
= - 554.52 kilojoules

hence, work done = -554.52kJ