Chapter 13, Problem 9RE

The pressure in newtons per square meter $\left(N/m_2\right)$ of a gas in a cylinder is given by $P=10T/V$ with T in kelvins (K) and V in cubic meters $\left(m^3\right).$

(a) If T is increasing at a rate of $3K/min$ with V held fixed at $2.5m^3,$ find the rate at which the pressure is changing when $T=50K.$

(b) If T is held fixed at $50K$ while V is decreasing at the rate of $3m^3/\min ,$ find the rate at which the pressure is changing when $V=2.5{\text{ m}}^3.$