The pressure, volume, and temperature of a mole of an ideal gas are related by t

Question

The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV=8.31T, where P is measured in kilopascals, V in liters, and T in kelvins.  Use differentials to find the approximate change in pressure, if the volume increases from 14 liters to 14.4 liters, and the temperature decreases from 350 kelvins to 341 kelvins.

The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV=8.31T, where P is measured in kilopascals, V in liters, and T in kelvins. Use differentials to find the approximate change in pressure, if the volume increases from 14 liters to 14.4 liters, and the temperature decreases from 350 kelvins to 341 kelvins. The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV = 8.3IT, where P is measured in kilopascals, V in liters, and T in kehins. Use differentials to find the approximate change in pressure, if the volume increases from 14 liters to 14.4 liters, and the temperature decreases from 350 kehins to 341 kehins.

Explanation / Answer

Using partial variables,
So P=nRT (V^-1)
diff. wrt T
dP|v=nR(V^-1)*dT
diff wrt V
dP|t =-nR(V^-2)*dv T
so
dP=dP|v+dP|t = nR(V^-1)*dT - nR(V^-2)*dv
v=14, dv=0.4, T=350, dT=-9

i.e dP = -11.16 Kilo pascals..

i.e pressure decreases by 11.16 kPa..

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