Question

if i have 2.9 l of gas at a pressure of 5 atm and a temperature of 323 k, what will be the temperature of the gas if i decrease the volume of the gas to 2.4 l and decrease the pressure to 3 atm?
round to 3 sig figs. do not include units.
answer

Explanation:

Step1: Use the combined gas law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\). We need to solve for \(T_2\).

Step2: Rearrange the formula for \(T_2\)

From \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\), we get \(T_2=\frac{P_2V_2T_1}{P_1V_1}\).

Step3: Substitute the given values

Given \(P_1 = 5\), \(V_1=2.9\), \(T_1 = 323\), \(P_2=3\), \(V_2 = 2.4\).
\(T_2=\frac{3\times2.4\times323}{5\times2.9}\)
First calculate the numerator: \(3\times2.4\times323=3\times775.2 = 2325.6\)
Then calculate the denominator: \(5\times2.9=14.5\)
\(T_2=\frac{2325.6}{14.5}\approx160.386\)

Answer:

160