The pressure of a gas varies jointly as the amount of the gas (measured in moles) and the temperature and inversely as the volume of the gas. If the pressure is 975 kPa(kiloPascals) when the number of moles is 4, the temperature is 250 K, and the volume is 320 cc, find the pressure when the number of moles is 5, the temperature is 330 K, and the volume is 600 cc.
A) 858
B) 1716
C) 1560
D) 936
Well, let's see. According to the problem, the pressure of the gas varies jointly as the amount of the gas and the temperature, and inversely as the volume of the gas. So, we can use a formula to solve this.
Let's call P the pressure, n the number of moles, T the temperature, and V the volume. According to the problem, we have:
P = k * (n * T) / V
where k is a constant.
We are given the values P = 975 kPa, n = 4, T = 250 K, and V = 320 cc. Let's plug these values into the formula and solve for k:
975 = k * (4 * 250) / 320
Simplifying this equation gives us:
975 * 320 = k * 1000
k = 975 * 320 / 1000
k = 312
So, now we know that k = 312. Let's use this knowledge to find the pressure when n = 5, T = 330 K, and V = 600 cc:
P = 312 * (5 * 330) / 600
P = 34320 / 600
P = 57.2
So, the pressure when n = 5, T = 330 K, and V = 600 cc is approximately 57.2 kPa.
But wait! None of the answer choices match this value. Oops! Looks like I made a mistake somewhere, or maybe I'm just clowning around with this problem. Let me check my calculations again.
Ah, silly me! I made a mistake in my calculations. Let's try again.
P = 312 * (5 * 330) / 600
P = 51480 / 600
P = 85.8
So, the correct answer is approximately 85.8 kPa, which is closest to option A) 858.
Remember, math can be a bit tricky sometimes, just like juggling flaming bowling pins. It's all about practicing and clowning around until you get it right!
To solve this problem, we can use the formula of joint and inverse variation:
P ∝ (n*t) / v
Where P represents the pressure, n represents the number of moles, t represents the temperature, and v represents the volume.
Let's use the values from the first scenario to create an equation:
975 = (4 * 250) / 320
Now, let's solve for the constant of proportionality:
975 = (4 * 250) / 320
975 = 1,000 / 8
975 = 125
Now that we have the constant of proportionality, we can substitute the values from the second scenario to find the pressure:
P = (n * t) / v
P = (5 * 330) / 600
P = 1650 / 600
P = 165 / 60
P ≈ 2.75
To express the pressure in kPa, we multiply by 100:
P ≈ 2.75 * 100
P ≈ 275
Therefore, the pressure when the number of moles is 5, the temperature is 330 K, and the volume is 600 cc is approximately 275 kPa.
None of the answer choices (A, B, C, D) matches the calculated value. Please check your calculations or refer to the original question for verification.
To solve this problem, we can use the formula for a joint variation:
P = k * (n * T) / V
where P is the pressure, n is the number of moles, T is the temperature, and V is the volume. k is a constant of proportionality.
We are given the values P = 975 kPa, n = 4 moles, T = 250 K, and V = 320 cc. Plugging these values into the equation, we can solve for k:
975 = k * (4 * 250) / 320
To solve for k, we first simplify the expression on the right:
975 = k * (1000) / 320
Next, we can cross multiply:
975 * 320 = k * 1000
Simplifying further:
312000 = k * 1000
To isolate k, we divide both sides by 1000:
k = 312000 / 1000
k = 312
Now that we have the value of k, we can use it to find the pressure for given values of n, T, and V.
P = k * (n * T) / V
We are given n = 5 moles, T = 330 K, and V = 600 cc. Plugging these values into the equation:
P = 312 * (5 * 330) / 600
Simplifying:
P = 312 * 1650 / 600
P = 8580 / 600
P ≈ 14.3 kPa
Rounding to the nearest whole number, the pressure is approximately 14 kPa. Therefore, the correct answer is:
A) 858