Ideal Gas Law The pressure P . temperature T , and volume

Chapter 4, Problem 44E

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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 \(\Delta T=0.05\). 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 \(\Delta V=0.1\). 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 \(\Delta V=0.1\). What is the approximate change in the temperature? Does the temperature increase or decrease?

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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 \(\Delta T=0.05\). 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 \(\Delta V=0.1\). 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 \(\Delta V=0.1\). What is the approximate change in the temperature? Does the temperature increase or decrease?

ANSWER:

SOLUTION Given P = T V STEP 1 (a). Here Volume is held constant.Thus P is a function of T. Therefore we can write P(T) = T V P (T) = 1 V Now the increase in temperature, T = 0.05 The approximate change in pressure is given by P = P (T)T = 0.05 V This is a positive quantity.Thus the pressure increases with the increase in temperature. STEP 2 (b). Here temperatu

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