A balloon under constant pressure goes from a very cold freezer at 150 K to a hot car at 300 K.
A. Volume increases 150 P
B. Volume doubles
C. Volume is cut in half
D. Volume stays the same
Based on the given scenario, the ideal gas law can be applied to determine the change in volume. The ideal gas law is represented as 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.
Since the pressure is constant, P does not change.
The initial temperature T1 is 150 K, and the final temperature T2 is 300 K.
V1/T1 = V2/T2
Using the above equation, we can solve for V2.
V2 = (V1 * T2) / T1
Since V1 and T1 are both non-zero values, we can determine the relationship between V1 and V2 based on the ratio T2/T1.
If T2 is twice as much as T1 (as in the given scenario), then T2/T1 = 2. Therefore, V2 = 2 * V1.
This implies that the volume doubles (B) when the balloon goes from the very cold freezer at 150 K to the hot car at 300 K.
To determine how the volume of the balloon changes when it goes from a very cold freezer at 150 K to a hot car at 300 K, we can use the ideal gas law. The ideal gas law states that 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.
Since the pressure is constant, we can rearrange the ideal gas law to solve for the volume change:
V1 / V2 = T1 / T2
Where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
Using the given temperature values, we have:
V1 / V2 = 150 K / 300 K
V1 / V2 = 1/2
Therefore, the volume of the balloon is cut in half (C) when it goes from the very cold freezer at 150 K to the hot car at 300 K.
To determine the effect of temperature change on the volume of a balloon under constant pressure, we can use the ideal gas law 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
- T is the temperature in Kelvin
In this case, the pressure is constant, so we can rewrite the equation as:
V1/T1 = V2/T2
We know that the temperature of the freezer is 150 K (T1) and the temperature of the hot car is 300 K (T2).
Let's substitute these values into the equation and simplify:
V1/150 = V2/300
To find the ratio of the volumes, we can cross multiply:
300 * V1 = 150 * V2
Now, we can compare the values to determine the relationship between the initial volume (V1) and the final volume (V2):
If V1 is greater than V2, the volume would decrease (C. Volume is cut in half).
If V1 is less than V2, the volume would increase (A. Volume increases 150%).
If V1 is equal to V2, the volume would stay the same (D. Volume stays the same).
Therefore, the answer is D. Volume stays the same.