The temperature of an enclosed gas at constant pressure changes from 200 K to 800 K. What happens to the volume of the gas? a The volume will decrease to one-half (1/2) of its original volume. b The volume will increase to 4 times its original volume. c The volume will decrease to one-fourth (1/4) of its original volume. d The volume will increase to 2 times its original volume. e The volume will stay the same.
According to Charles's Law, at constant pressure, the volume of a gas is directly proportional to its temperature. Therefore, as the temperature of the gas increases from 200 K to 800 K, the volume of the gas will increase.
The correct answer is:
d) The volume will increase to 2 times its original volume.
To determine what happens to the volume of the gas, we can use the ideal gas law, which 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 this scenario, the pressure is constant, so we can simplify the equation to V/T = constant.
Given that the temperature changes from 200 K to 800 K, let's calculate the ratio of the final volume (V2) to the initial volume (V1).
V2/T2 = V1/T1
V2/V1 = T2/T1
V2/V1 = 800 K / 200 K
V2/V1 = 4
Therefore, the volume of the gas will increase to 4 times its original volume. Therefore, the correct answer is (b) The volume will increase to 4 times its original volume.
To determine what happens to the volume of an enclosed gas when the temperature changes at constant pressure, we can refer to 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 this case, the pressure is constant, so the equation can be simplified to V / T = nR / P. Since n, R, and P are all constant, we can rewrite the equation as V / T = k, where k is a constant.
Now, let's analyze the given temperature change. The temperature changes from 200 K to 800 K. If the temperature increases by a factor of 4 (from 200 to 800), the volume must also increase by the same factor to keep the equation V / T = k true.
Therefore, the correct answer is d) The volume will increase to 2 times its original volume.