You visited us 1 times! Enjoying our articles? Unlock Full Access!

Work Done in Isothermal Reversible Process

One mole of a...

Question

One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is $w_{s}$ and that along the dotted line path is $w_{d}$ , then the value close to the ratio $\frac{w_{d}}{w_{s}}$ is-
(Take $l o g 11 = 1.04$ )

1.8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4.8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5.5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6.2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A 1.8
Work done in both the paths is done by the gas as volume is expanding so work done will be negative and is given as
$d w = - P d V$
In the P-V graph work done will be equal to area under the curve since area cannot be negative we will consider the magnitude of work done only.
Now, work done along path of solid line is reversible in nature while along the dashed line it is irreversible.

So, for irreversible, work done is equal to the sum of areas of the three rectangles i.e :

$W_{d} = (4 \times 1.5) + (0) (1 \times 1) (\frac{1}{2} \times 2.5)$ = $\frac{33}{4} L a t m$

For the process along the solid line (reversible) work is given as,
$W_{s} = 2.303 \times P_{1} V_{1} l o g \frac{V_{2}}{V_{1}}$
$= 2.303 \times 4 \times 0.5 \times l o g \frac{5.5}{0.5}$
$= 4.6 \times l o g (11) L a t m$

So, $\frac{W_{d}}{W_{s}} = \frac{33}{4 \times 4.6 \times 1 o g 11} = 1.72 (a p p r o x .)$

Suggest Corrections

Similar questions

Q. One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is

w_{s}

and that along the dotted line path is

w_{d}

, then the value close to the ratio

\frac{w_{d}}{w_{s}}

is-
(Take

l o g 11 = 1.04

)

Q. One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is

W_{s}

and that along the dotted line path is

W_{d}

then the integer closest to the ratio

\frac{W_{d}}{W_{s}}

is:___

Q. One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph above. If the work done along the solid line path is

w_{s}

and that along the dotted line path is

w_{d}

, then the integer closest to the ratio

w_{d} / w_{s}

is :

Q. One mole of an ideal gas is taken from a to b along two paths denoted by the solid and dashed line as shown in the graph above. If the work done along the solid line path is

w_{s}

and that along the dotted line path is

w_{d}

, then the integer closest to the ratio

w_{d} / w_{s}

is:

One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. It the work done along the solid line path is $W_{s}$ and that along the dotted line path is $\frac{W_{d}}{W_{s}}$ is ___

Join BYJU'S Learning Program

One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is ws and that along the dotted line path is wd, then the value close to the ratio wdws is- (Take log11=1.04)