Question

An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The condition at the start and at the end of the process with usual notation are: $P_1=100\text{kPa},V_1=0.2{\text{m}}^3$ and $P_2=150\text{kPa},V_2=0.1{\text{m}}^3$ and the gas constant $R=8.314\text{J/mol K}$. The magnitude of the work required for the process is

• A. $15\text{kJ}$
• B. $10\text{kJ}$
• C. $2.5\text{kJ}$
• D. $12.5\text{kJ}$

Answer 1

The correct option is D $12.5\text{kJ}$

Given that
$P_1=100\text{kPa},V_1=0.2{\text{m}}^3$
$P_2=150\text{kPa},V_2=0.1{\text{m}}^3$
$P-V$ diagram will be a straight line.


Work done = Area under the $P-V$ diagram
= Area of $abcd$ + area of $cde$
$=(100\times 0.1)+(\frac{1}{2}\times 0.1\times 50)$
$=10+2.5$
$=12.5\text{kJ}$
The work is done on the gas, since the process is compression.