what is the initial temperature (in degrees C) of a system that has the pressure decreased by 10 times while the volume increased by 5 times with a final temperature of 150 K?

Question

what is the initial temperature (in degrees C) of a system that has the pressure decreased by 10 times while the volume increased by 5 times with a final temperature of 150 K?

a)27
b)75
c)300
d)-198
e) none of the above

Please explain--I need to know how to do this--this is only a practice question.

Answer 1

To solve this problem, we can use the Ideal Gas Law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature

Since we are given that the pressure decreased by 10 times, the new pressure (P') is equal to 1/10 times the initial pressure (P):

P' = P/10

We are also given that the volume increased by 5 times, so the new volume (V') is equal to 5 times the initial volume (V):

V' = 5V

Given that the final temperature (T') is 150 K, we can use the equation to solve for the initial temperature (T).

We rearrange the equation to isolate T:

T = PV / (nR)

And since we are not given any information about the number of moles of gas, we can consider it constant. Thus, the equation simplifies to:

T = (PV) / R

Now, let's substitute the new values into the equation:

T' = (P' * V') / R
150 K = (P/10 * 5V) / R

Since we know that P' = P/10 and V' = 5V, we can substitute:

150 K = (P' * V') / R
150 K = (P/10 * 5V) / R

Now, we can cancel out V and R:

150 K = (P * 5) / (10 * R)
150 K = (P * 5) / (5 * R)

Finally, we can cancel out 5:

150 K = P / R

Now, we can solve for the initial pressure (P) by substituting the final temperature (T'):

150 K = P / R

Now, we can substitute the values into the equation to solve for P:

150 = P / R

P = 150 * R

Since temperature is in Kelvins, we need to convert it to degrees Celsius by subtracting 273.15:

P = 150 * 8.314 = 1247.1 Pa

Therefore, the initial temperature of the system is 1247.1 degrees Celsius.

None of the given choices (a), (b), (c), (d) are correct. So, the correct answer is (e) none of the above.

Answer 2

To solve this question, we can use the ideal gas law equation: PV = nRT, where P represents pressure, V represents volume, n represents the number of moles, R is the gas constant, and T represents temperature.

We can assume that the number of moles and the gas constant remain constant in this scenario. Therefore, we can rewrite the ideal gas law equation as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

In this problem, we are given that the pressure is decreased by 10 times (P2 = P1/10) and the volume is increased by 5 times (V2 = 5V1). We also know that the final temperature is 150 K (T2 = 150 K).

To find the initial temperature T1, we need to rearrange the ideal gas law equation to solve for T1.

P1V1 = P2V2
P1V1 = (P1/10)(5V1)
10P1V1 = P1*5*V1
10V1 = 5V1
10 = 5

Now, we have found that the initial temperature is 5 times the final temperature. Therefore:

T1 = 5 * T2
T1 = 5 * 150 K
T1 = 750 K

However, the given options are in degrees Celsius, so we need to convert the result from Kelvin to Celsius.

T1 = 750 K - 273.15
T1 ≈ 476.85°C

Since none of the given options match, the correct answer would be e) none of the above.

Answer 3

Use (P1V1)/T1 = (P2V2)/T2

Make up values for those not listed, then multiply or divide by 10 or 5 to obtain the new values. Don't forget to use Kelvin for temperature. When you solve for the final T, remember to subtract 273 to change Kelvin back to C.