Differentials

**fearless901** · Apr 21st 2009, 07:06 PM

Question: The pressure, volume and temp. of an ideal gas are related by the equation: PV=nRT. where P is menasured in KPA(kilo pascals), V in liters, and T in kelvins. Use differentials to find the approximate change in the pressure if the volume increases from 12L to 12.3L and the temperature decreses from 310K to 305K. Any idea how to do this?
Thank you

**Calculus26** · Apr 21st 2009, 07:47 PM

P = nRT/V

dP = dP/dT dT + dP/dV dV where dP/dT and dP/dV are actually partial derivatives

dP = (nR/V)dT - (nRT/V^2)dV

Fill in the data and you're done

**fearless901** · Apr 21st 2009, 07:50 PM

thank you

**TheEmptySet** · Apr 21st 2009, 08:08 PM

Originally Posted by fearless901

Question: The pressure, volume and temp. of an ideal gas are related by the equation: PV=nRT. where P is menasured in KPA(kilo pascals), V in liters, and T in kelvins. Use differentials to find the approximate change in the pressure if the volume increases from 12L to 12.3L and the temperature decreses from 310K to 305K. Any idea how to do this?
Thank you

$P=\frac{nRT}{V}$

$dP=\frac{\partial P}{\partial V}dV+\frac{\partial P}{\partial T}dT$

$dP=-\frac{nRT}{V^2}dV+\frac{nT}{V}dT$

from here just plug in the values and you are done.

EDIT: WOW I was really late hehe

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