Suppose it is a hot summer day (40.0 degrees C = 104.0 degrees F), and you have left a can of hairspray outside so the gas within it is now at the same temperature of its surroundings. As part of your chemistry lab class, you have to build a safe and effective potato gun to share with the local elementary school, and you must be sure that the combustion chamber is well insulated and will not harm (burn) the shooter. You spray the warm hairspray into the 3.50 L chamber on your gun. You seal the cap, then ignite it, and the resulting gas expands to 13.0 L as the potato is shot out. What is the final temperature, in Celsius, inside the combustion chamber? What is this temperature in Fahrenheit? [SHOW ALL WORK TO RECEIVE CREDIT]

Question

Suppose it is a hot summer day (40.0 degrees C = 104.0 degrees F), and you have left a can of hairspray outside so the gas within it is now at the same temperature of its surroundings. As part of your chemistry lab class, you have to build a safe and effective potato gun to share with the local elementary school, and you must be sure that the combustion chamber is well insulated and will not harm (burn) the shooter. You spray the warm hairspray into the 3.50 L chamber on your gun. You seal the cap, then ignite it, and the resulting gas expands to 13.0 L as the potato is shot out. What is the final temperature, in Celsius, inside the combustion chamber? What is this temperature in Fahrenheit? [SHOW ALL WORK TO RECEIVE CREDIT]

Answer 1

see prior question

Answer 2

To find the final temperature inside the combustion chamber, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin

First, let's convert the initial and final volumes from liters to cubic meters:
3.50 L = 0.00350 m^3
13.0 L = 0.0130 m^3

Given that the initial and final temperatures are the same (since the hairspray and surroundings were at the same temperature), we'll denote it as T_initial = T_final = T.

Now let's rearrange the ideal gas law equation to solve for the final temperature:

T_final = (PV) / (nR)

We need to determine the number of moles of gas in the combustion chamber. To do this, we'll use the ideal gas equation in terms of moles:

PV = NRT

Where N is the number of moles.

We can rewrite the equation as:

N_initial = (PV) / (RT_initial)
N_final = (PV) / (RT_final)

Since the number of moles of gas remains constant, we have:

N_initial = N_final

Substituting the respective equations for N, we get:

(PV) / (RT_initial) = (PV) / (RT_final)

Now we can cancel out the common terms and solve for T_final:

1 / T_initial = 1 / T_final

Cross multiplying, we have:

T_final = (T_initial * T) / (T_initial)

Since T_initial = T_final, we can simplify to:

T_final = T

Therefore, the final temperature (T_final) inside the combustion chamber is the same as the initial temperature (T_initial). Therefore, the final temperature inside the combustion chamber is 40.0 degrees Celsius or 104.0 degrees Fahrenheit.