Question

Problem 1. The ideal gas law states PV nRT where P, V, and T are the pressure, volume and absolute temperature; n is the number of moles of gas; and R is the the ideal gas constant. Consider a 1-gallon canister of gas at a pressure of 1 atm. Answer the following questions: 1. How much energy would be needed to increase the pressure of the closed canister to 50 psi without changing its volume? Express your answer in SI units 2. How much would the absolute temperature rise by? Express in percentage increase.

Problem 1: Ideal Gas Law

Answer 1

(a) Initial pressure (P₁) = 1 atm = 1.013*10⁵ bar
Volume (V) = 1 gallon = 0.00378 m³
Consider the mole of gas = 1
Using ideal gas equation
PV = nRT
(1.013*10⁵ )*(0.00378) = 1*8.314*T
T₁ = 46.057 K
Now the pressure is raised to (P₂) = 50 psi = 3.447*10⁵ Pa
Using ideal gas equation
(3.447*10⁵ )*(0.00378) = 1*8.314*T₂
T₂ = 156.737 K
We know that the energy at constant volume is given by
Q = nC_V*(T₂ - T₁)
(b)
We know that percentage change in temperature would be
$=\left ( \frac{T_{2} - T_{1}}{T_{1}} \right )*100$
$=\left ( \frac{156.737 - 46.057}{46.057} \right )*100$
= 240.31 %
hence the temperature increased by 240.31 %.