53 RT 1. Use the ideal gas law P= with volume V in cubic inches (in”), temperature T in V Kelvins (K) and R=10(in.lb/K ) to find the rate at which the temperature of a gas is changing when the volume is 200 in' and increasing at the rate of 4 in /s, while the pressure is 5lb/in and decreasing at the rate of ilb/in/s.
Answers
Answer:
95/85
Step-by-step explanation:
Given:
The rate at which the volume is increasing = 4 in³/s
The rate at which the pressure is decreasing = 5 lb/s
To Find:
The rate at which the temperature of the gas is changing
Solution:
The temperature of the gas is decreasing at the rate of 1 Kelvin per second.
An ideal gas is one that follows the ideal gas equation at all temperatures and pressures.
The ideal gas equation is represented as PV = nRT
Here, P = Pressure of the gas
V = Volume of the gas
n = Number of moles of the gas
R = The universal gas constant
T = Absolute temperature of the gas
The equation can be represented as:
ΔP/Δt . ΔV/Δt = nR . ΔT/Δt (n and R are constants)
Substituting ΔP/Δt, ΔV/Δt, and n by -5 lb/s, 4 in³/s, and 1 respectively, we get:
-5 X 4 = R . ΔT/Δt
or -10 = 10 . ΔT/Δt (Given that R = 10in.lb/K)
or ΔT/Δt = -1 K/s