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The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 8.0 atm and is increasing at a rate of 0.13 atm/min and V = 14 L and is decreasing at a rate of 0.17 L/min. Find the rate of change of T with respect to time at that instant if n = 10 moles.

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  1. PV = nRT

    V dP/dt + P dV/dt = nR dT/dt

    Now just plug in the data:

    (14)(0.13) + (8.0)(-0.17) = (10)(0.0821) dT/dt
    dT/dt = 0.56 °K/s

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