Ideal Gas Law The pr?essure P ? . tempe?rature T? , and v?olume V? of an ideal gas are related by ? P? V =? RT? , where ?n is the number of moles of the ?gas and ?R is the universal gas constant. For the purposes of this exerc ? ise, let ?n? 1; thus, ? = ?T/V. a. Suppose that the volume is held constant and the temperature increases by ? ?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 ? ??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 ??V = 0.1. What is the approximate change in the temperature? Does the temperature increase or decrease?

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 temperature is held constant.Thus P is a function of V. T Therefore we can write P(V) = V P (V) = V2 Now the increase in temperature, V = 0.1 The approximate change in pressure is given by P = P (V)V = 0.1T V2 This is a negative quantity.Thus the pressure decreases with the increase in volume. STEP 3 (c). Here pressure is held constant. We have to find the approximate change in temperature.Thus we can rewrite the equation as T = PV Since the pressure is constant here T is a function of V Therefore we can write T(V) = PV T (V) = P Now the increase in temperature, V = 0.1 The approximate change in temperature is given by T = T (V)V = 0.1P This is a positive quantity.Thus the temperature increases with the increase in volume.