Question

500 J of work must be done to compress a gas to half its initial volume at constant temperature. How much work must be done to compress the gas by a factor of 10, starting from its initial volume?

Short answer

The value of work done energy is 1661J

Step-by-step solution

Definition of work done energy 

The work done has represented as energy that is transferred between system and environment. If energy goes from gas to environment then it is positive and if energy goes from environment to gas.

Step  2: Finding the work done energy.

The relation of work done energy with isolate gas is

$\begin{array}{rcl}W& =& -nRT\ln \frac{V_2}{V_1}\end{array}$

Now $V_2=0.5V_1$

$\begin{array}{rcl}nRT& =& \ln \frac{(0.5V_1)}{V_1}\times -500J\\ & =& 721.34j\end{array}$

Applying the value of $V_2=\frac{1}{10}$

the work done energy is

$\begin{array}{rcl}W& =& -721.34\times \ln \frac{(1/10)V_1}{V_1}\\ & =& 1161J\end{array}$

The value of work done energy is 1661J