My textbook gave me a different answer and I don't know what I did wrong.
Q. Your tires are adjusted to 227.5kPa at 10 degrees Celsius in the mechanic's garage. You then take your car home and park it outside. The overnight temperature drops to -5 degree celsius. Determine the new tire pressure?
I did Gay-Lussac Law and I got 215.45kPa. My texbook answer is 2.2 x 10*2kPa
2.2*10^2 = 220 close enough
but anyway
P V = n RT
V, n and R are the same before and after so
agree P2 = P1 (T2/T1)
T1 = 10 C = 293 K
T2 = -5 C = 268 K
so
P2 = (268/293)* 227.5 k pascals
= 223.3 k Pa which rounds to 2.2*10^2
To solve this problem, you can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature when the volume and the amount of gas is constant. The formula for the ideal gas law is:
P1/T1 = P2/T2
Where:
P1 is the initial pressure of the gas
T1 is the initial temperature of the gas
P2 is the final pressure of the gas
T2 is the final temperature of the gas
First, convert the initial temperature and final temperature to Kelvin by adding 273.15 to each temperature.
Initial Temperature (T1) = 10°C + 273.15 = 283.15 K
Final Temperature (T2) = -5°C + 273.15 = 268.15 K
Now, let's substitute the known values into the formula and solve for P2:
P1/T1 = P2/T2
227.5 kPa / 283.15 K = P2 / 268.15 K
Cross multiply and solve for P2:
P2 = (227.5 kPa * 268.15 K) / 283.15 K
P2 = 214.757 kPa
When rounded to two decimal places, the new tire pressure is approximately 214.76 kPa.
It seems that the answer you provided using Gay-Lussac's Law is very close to the correct answer. The difference could be due to rounding errors or variations in calculations. However, the textbook answer of 2.2 x 10^2 kPa is not an accurate solution.
To solve this problem, we can use the ideal gas law, which states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperatures to Kelvin. To do this, we add 273.15 to the Celsius temperatures.
10 degrees Celsius + 273.15 = 283.15 K
-5 degrees Celsius + 273.15 = 268.15 K
Next, let's compare the initial and final states of the gas:
Initial Conditions:
Pressure (P1) = 227.5 kPa
Temperature (T1) = 283.15 K
Final Conditions:
Pressure (P2) = ?
Temperature (T2) = 268.15 K
Now, we can rearrange the ideal gas law to solve for the final pressure (P2):
P2 = (P1 * T2) / T1
Plugging in the values:
P2 = (227.5 kPa * 268.15 K) / 283.15 K
Calculating this, we find:
P2 = 215.37 kPa (rounded to two decimal places)
Therefore, based on the calculations, the new tire pressure is approximately 215.37 kPa.
Regarding the discrepancy between your answer and the textbook's answer, it is possible that there was a rounding error or a mistake in the calculation. Make sure to double-check your calculations and ensure that you are using the correct values for the temperatures in Kelvin.