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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.8, Problem 35E

To determine

**To find:** The rate of change of *T* with respect to time if *n* = 10 mol.

Expert Solution

The rate of change of *T* with respect to time if *n* = 10 mol is approximately −0.2436 K/min.

**Given:**

The gas law for an ideal gas is given by *PV* = *nRT*, where *T* is absolute temperature in Kelvins, *P* is pressure in atmosphere, *V* is volume in liters, *n* is the number of moles of the gas and the value of gas constant *R* = 0.0821.

Also given that *P* = 8 atm and *V* = 10 L,

**Calculation:**

An ideal gas function is given by *PV* = *nRT*.

Express the function in terms of T as,

Substitute, *R* = 0.0821 and *n* = 10,

Obtain the derivative of *T* with respect to *t* as follows,

Substitute the respective values in the equation (1),

Thus, the derivative,