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, wh

Question

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 = 13 L and is decreasing at a rate of 0.17 L/min. Find the rate of change of T with respect to time (in K/min) at that instant if n = 10 mol.

in progress 0
Thanh Hà 5 years 2021-07-11T06:56:23+00:00 1 Answers 551 views 0

Answers ( )

  1. Thunguyet
    1
    2021-07-11T06:57:24+00:00
    Reply

    Answer:

    The rate of change of T with respect to time is 0.40 K/min

    Explanation:

    The gas law equation is:

    PV = nRT

    We can find the rate of change of T with respect to time by solving the above equation for T and derivating with respect to time:

    \frac{dT}{dt} = \frac{d}{dt}(\frac{PV}{nR})

    \frac{dT}{dt} = \frac{1}{nR}(V\frac{dP}{dt} + P\frac{dV}{dt})

    Where:

    n: is the number of moles = 10 mol

    R: is the gas constant = 0.0821

    V: is the volume = 13 L

    P: is the pressure = 8.0 atm

    dP/dt: is the variation of the pressure with respect to time = 0.13 atm/min

    dV/dt: is the variation of the volume with respect to time = -0.17 L/min

    Hence, the rate of change of T is:

    \frac{dT}{dt} = \frac{1}{10*0.0821}(13*0.13 - 8.0*0.17) = 0.40 K/min    

    Therefore, the rate of change of T with respect to time is 0.40 K/min

    I hope it helps you!    

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )