Chemistry students will recognize the ideal gas law, given by PV = nRT, which re

Question

Chemistry students will recognize the ideal gas law, given by PV = nRT, which relates Pressure (in Pascals), Volume (in Liters), and Temperature (in degrees Kelvin) of n moles of gas where R is the ideal gas constant. Thus, we can view pressure (in Pa), volume (in L), and temperature (in K) as variables, each one dependent on the other two. a. If pressure of a gas is increasing at a rate of 1.4 Palmin and temperature is increasing at a rate of 1.4 K/min, how fast is the volume changing? Submit Answer Incorrect. Tries 1/10 Previous Tries b. If the volume of a gas is decreasing at a rate of 1.5 L/min and temperature is increasing at a rate of 0.1 K/min, how fast is the pressure changing?

Explanation / Answer

PV = nRT

V = nRT/P

Deriving with time :
dV/dt = nR * d/dt(T/P)

dV/dt = nR * [PdT/dt - TdP/dt]/P^2

nR * [1.4P - 1.4T) / P^2

So, V' = 1.4*n*R(P - T)/P^2 -----> ANS

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b)
P = nRT/V

P' = nR(TdV/dt - VdT/dt)/V^2

Now, plug in :
P' = nR(-1.5T - 0.1V)/V^2

P' = -0.1nR(15T + V)/V^2 ----> ANS

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