(b) (4 pts.) 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]
Is this a take home quiz? I would look at (V1/T1) = (V2/T2)
Suppose it is a hot summer day (104.0 oF), 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 2.50 L chamber on your gun. You seal the cap, then ignite it, and the resulting gas expands to 12.0 L as the potato is shot out.
What is the final temperature, in Celsius, inside the combustion chamber?
What is this temperature in Fahrenheit?
To solve this problem, we can use the gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
where:
P1 = initial pressure of the gas (atmospheres)
V1 = initial volume of the gas (liters)
T1 = initial temperature of the gas (Kelvin)
P2 = final pressure of the gas (atmospheres)
V2 = final volume of the gas (liters)
T2 = final temperature of the gas (Kelvin)
First, we need to convert the initial temperature from Celsius to Kelvin:
T1 = 40.0 + 273 = 313 K
Next, we can plug in the known values into the gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Since the hairspray is left outside and the gas within it is at the same temperature as its surroundings, we can assume that the external pressure is equal to the internal pressure. Therefore, P1 = P2.
Substituting the given values:
(P1 * V1) / T1 = (P1 * V2) / T2
Since P1 = P2, we can simplify the equation further:
(V1) / T1 = (V2) / T2
Now, we can solve for T2 by rearranging the equation:
T2 = (V2 * T1) / V1
Plugging in the values:
T2 = (13.0 * 313) / 3.50
T2 ≈ 1166.86 K
Finally, let's convert the final temperature from Kelvin to Celsius:
T2 = 1166.86 - 273
T2 ≈ 893.86 °C
To convert from Celsius to Fahrenheit, we can use the equation:
°F = (°C * 9/5) + 32
Plugging in the value we obtained:
°F = (893.86 * 9/5) + 32
°F ≈ 1641.94 °F
Therefore, the final temperature inside the combustion chamber is approximately 893.86 °C (or 1641.94 °F).