Question

An ideal gas occupies a volume of $2{\mathrm{m}}^3$ at a pressure of $3\times {10}^6\mathrm{Pa}$. The energy of the gas is:

Answer 1

Step 1: Given data

The volume occupied by an ideal gas = $2{\mathrm{m}}^3$

The pressure of ideal gas = $3\times {10}^6\mathrm{Pa}$

Step 2: Formula used

The internal energy of a gas is given by the formula: $\mathrm{E}=\frac{3}{2}\mathrm{PV}$ where

$\mathrm{E}=\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{gas}$

$\mathrm{P}=\mathrm{pressure}$

$\mathrm{V}=\mathrm{volume}$

Step 3: Calculations

Putting the values in the formula $\mathrm{E}=\frac{3}{2}\mathrm{PV}$

$$\begin{gathered} \Rightarrow \mathrm{E}=\frac{3}{2}\times 3\times {10}^6\times 2 \\ \Rightarrow \mathrm{E}=9\times {10}^6\mathrm{J} \end{gathered}$$

Hence, the energy of the gas is $9\times {10}^6\mathrm{J}$.