In a classical equation from chemistry, the pressure of a gas is proportional to the product of the volume of the gas and the temperature of the gas. In symbols, P = kVT for some constant k. How fast is the pressure changing at an instant when the volume is 20 mL and increasing at 3 mL/min and the temperature is at 21 degrees C and is decreasing at a rate of 2 degrees per minute? Assume that k = 0.8 kilograms per mL-degree.
A) increasing at 18.4 kilograms/min
B) increasing at 14.4 kilograms/min
C) decreasing at 23.5 kilograms/min
D) decreasing at 12.8 kilograms/min
E) increasing at 12.7 kilograms/min

Question

Quizplus · Accepted Answer

The pressure is changing at a rate of 18.4 kilograms/min. This is because the volume is increasing at a rate of 3 mL/min and the temperature is decreasing at a rate of 2 degrees per minute. The constant k is 0.8 kilograms per mL-degree. So, the rate of change of pressure is:dP/dt = k * (dV/dt * T + V * dT/dt)= 0.8 * (3 * 21 + 20 * (-2))= 18.4 kilograms/min

In a Classical Equation from Chemistry, the Pressure of a Gas