Chapter 3 - Section 3.7 - Rates of Change in the Natural and Social Sciences - 3.7 Exercises - Page 236: 37

The temperature is changing at a rate of $-0.24~K/min$

$PV = nRT$ $nR~\frac{dT}{dt} = P\frac{dV}{dt} + V\frac{dP}{dt}$ $\frac{dT}{dt} = \frac{P\frac{dV}{dt} + V\frac{dP}{dt}}{nR}$ $\frac{dT}{dt} = \frac{(8.0)(-0.15) + (10)(0.10)}{(10)(0.0821)}$ $\frac{dT}{dt} = -0.24~K/min$ The temperature is changing at a rate of $-0.24~K/min$