Answer:
The rate of change of T with respect to time is 0.40 K/min
Explanation:
The gas law equation is:
[tex] PV = nRT [/tex]
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:
[tex] \frac{dT}{dt} = \frac{d}{dt}(\frac{PV}{nR}) [/tex]
[tex] \frac{dT}{dt} = \frac{1}{nR}(V\frac{dP}{dt} + P\frac{dV}{dt}) [/tex]
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:
[tex] \frac{dT}{dt} = \frac{1}{10*0.0821}(13*0.13 - 8.0*0.17) = 0.40 K/min [/tex]
Therefore, the rate of change of T with respect to time is 0.40 K/min
I hope it helps you!
