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.

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

Explanation:

The gas law equation is:

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:

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:

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

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mechanics (greek   is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. the scientific discipline has its origins in ancient greece with the writings of aristotle and archimedes[1][2][3] (see history of classical mechanics and timeline of classical mechanics). during the early modern period, scientists such as galileo, kepler, and newton laid the foundation for what is now known as classical mechanics. it is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light. it can also be defined as a branch of science which deals with the motion of and forces on objects. the field is yet less widely understood in terms of quantum theory.

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