The pressure P, temperature T, and volume V of an ideal gas are related by PV=nR

Question

The pressure P, temperature T, and volume V of an ideal gas are related by PV=nRT, where n is the number of moles of the gas and R is the universal gas constant. For the purposes of this exercise, let nR=1, thus P=T/V. a. Suppose that the volume is held constant and the temperature increases by dT=0.05 What is the approximate change in the pressure? Does the pressure increase or decrease? b. Suppose that the temperature is held constant and the volume increases by dV=0.1 What is the approximate change in the pressure? Does the pressure increase or decrease? c. Suppose that the pressure is held constant and the volume increases by dV=0.1 What is the approximate change in the temperature? Does the temperature increase or decrease?

Explanation / Answer

P=T/V VP = T VdP + PdV = dT as V = constant dV=0 VdP=dT dP = 0.05/V pressure also increase by 0.05/V if T = constant dT=0 VdP=-PdV dP =-Px0.1/V = -P/(10xV) so pressure decreases as volume increases P= constant dP =0 PdV=dT dT= 0.1x P Temperature increases

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