Question 560: Thermodynamics & KTG

Question

In a certain thermodynamical process, the pressure of a gas depends on its volume as kV
3
. The work done when the temperature changes from 100$$^\circ$$C to 300$$^\circ$$C will be ___________ nR, where n denotes number of moles of a gas.

Accepted Answer

In this thermodynamical process, the pressure $ P $ of a gas is related to its volume $ V $ by the equation $ P = kV^3 $. Thus, we have:
$ PV^{-3} = k $
This implies that the value of $ x $ is $-3$ in the relationship. To find the work done ($ W $) when the temperature changes from 100ÃÂ°C to 300ÃÂ°C, we can use the formula:
$ W = \frac{nR(T_1 - T_2)}{x - 1} $
Substitute the given temperatures and the value of $ x $:
$ W = \frac{nR(100 - 300)}{-3 - 1} $
Calculate the expression:
$ W = \frac{nR(-200)}{-4} $
Which simplifies to:
$ W = 50 \, nR $

Thermodynamics & KTG

In a certain thermodynamical process, the pressure of a gas depends on its volume as kV 3 . The work done when the temperature changes from 100$^\circC to 300^\circ$C will be ___________ nR, where n denotes number of moles of a gas.

Integer / Numeric Answer Type