Question

the volume of one mole of an ideal gas changes from v to 2v at temperature 300k if R is universal gas constant then work done in process is ​

Answer 1

Answer:

$\boxed{\sf Work \ done = - 300Rln2}$

Given:

$\sf Initial \: volume \: (V_i )= V$

$\sf Final \: volume \: (V_f )= 2V$

Temperature (T) = 300 K

Moles of ideal gas (n) = 1

R is universal gas constant

To Find:

Work done in the process

Explanation:

As the temperature is constant through out the process therefore it's an 'Isothermal Process'.

It's not specific in the question whether the process is reversible or irreversible. So, we will assume that process is reversible.

Now, we will further proceed to solve this question by considering the process as: Isothermal Reversible Process

Formula used to find work done of isothermal reversible process is:

$\sf W_{rev} = -nRTln \frac{V_f}{V_i}$

Substituting value of $V_f$, $V_i$, T & n in the formula:

$\sf \implies W_{rev} = - 1 \times R \times 300 \times ln \frac{2 \cancel{V}}{ \cancel{V}}$

$\sf \implies W_{rev} = - 1 \times R \times 300 \times ln 2$

$\sf \implies W_{rev} = - 300 Rln 2$