Question

An ideal gas expands isothermally from 10ñ3 m3 to 10ñ2 m3 at 300 K against a constant pressure of 105 Nmñ2. The work done on the gas is

Answer 1

$\checkmark$  Given:

An ideal gas expands isothermally from   10⁻³ N m³ to 10⁻² N m³ at 300 K against a constant pressure of 10⁵ N/m²

$\checkmark$  To Find:

The work done on the gas

$\checkmark$  Solution:

We know that,

$\red{\bigstar \ \boxed{\rm W=-P \Delta V}}$

Here,

• $\rm W = work \ done$
• $\rm P = pressure$
• $\rm \Delta V= change \ in \ volume$

According to the question,

We are asked to find the work done on the gas

So, we must find "W"

Given that,

An ideal gas expands isothermally from   10⁻³ N m³ to 10⁻² N m³ at 300 K against a constant pressure of 10⁵ N/m²

Hence,

• $\rm P=10^{5} \ N/m^{2}$

We know that,

$\longrightarrow \rm \Delta V=V_{f}-V_{i}$

Therefore,

• $\rm \Delta V=(10^{-2}-10^{-3}) \ N \ m^{3}$

Hence,

Substituting the values,

We get,

$\green{\implies \rm W=-10^{5} \times (10^{-2}-10^{-3}) \ J}$

On further simplification,

We get,

$\orange{\implies \rm W=-10^{5} \times (9 \times 10^{-3}) \ J}$

Hence,

$\pink{\rm \implies W=-900 \ J}$

Therefore,

The work done on the gas = -900 J