The Ideal Gas Law relates the pressure P, temperature T, and volume Vof an ideal gas via the equation PV = nRT, where n is the number of moles of the gas andR is the universal gas constant. To simplify matters, we will assume that nR = 1, and soP = T/V. (a) Assume that the volume of the gas V is held constant and the temperature is allowed to increase by ΔT = 0.05. Use a differential to find an expression for the approximatechange in the pressure. Does the pressure increase or decrease? (b) Assume that the temperature of the gas T is held constant and the volume is allowedto increase by ΔV = 0.10. Use a differential to find an expression for the approximatechange in the pressure. Does the pressure increase or decrease?
The Ideal Gas Law relates the pressure P, temperature T, and volume V
of an ideal gas via the equation PV = nRT, where n is the number of moles of the gas and
R is the universal gas constant. To simplify matters, we will assume that nR = 1, and so
P = T/V.
(a) Assume that the volume of the gas V is held constant and the temperature is allowed to increase by ΔT = 0.05. Use a differential to find an expression for the approximate
change in the pressure. Does the pressure increase or decrease?
(b) Assume that the temperature of the gas T is held constant and the volume is allowed
to increase by ΔV = 0.10. Use a differential to find an expression for the approximate
change in the pressure. Does the pressure increase or decrease?
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