Question

A gas expands from $5\mathrm{liter}$ to $105\mathrm{liter}$ at a constant pressure $100N{m}^{-2}$. The work done is

• A. $1\mathrm{joule}$
• B. $4\mathrm{joule}$
• C. $8\mathrm{joule}$
• D. $10\mathrm{joule}$

Answer 1

The correct option is D

$10\mathrm{joule}$

Step 1: Given data

Pressure, $P={10}^{2}N{m}^{-2}$

Initial volume of the gas, $V_1=5liter$

Final volume of the gas, $V_2=105liter$

Step 2: Calculating work done

Change in volume,

$$\begin{gathered} V=V_2-V_1 \\ V=105liter-5liter \\ V=100 \\ V={10}^{-1}{m}^3\left[\because 1m^3=1000liter\right] \end{gathered}$$

Work done is calculated as,

$\begin{array}{rcl}\mathrm{Work}\mathrm{done}& =& \mathrm{Pressure}\times \mathrm{Change}\mathrm{in}\mathrm{volume}\\ & =& {10}^{2}N{m}^{-2}\times {10}^{-1}{m}^3\\ & =& 10J\end{array}$

The work done is$10J$

Hence, option (d) is correct.