The balloon contains 0.30 {\rm mol} of helium starts at a pressure of 115 {\rm kPa} and rises to an altitude where the pressure is 55.0 {\rm kPa}, maintaining a constant 300 {\rm K} temperature.
(A)By what factor does its volume increase?
(B)How much work does the gas in the balloon do?
find the moles of helium from
PV=nRT
Now,knowing the moles, find the volume at the altitude. PV=nRT, solving for volume
To find the answers to these questions, we can use the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are related by the equation PV = nRT. Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Let's solve each part of the question step by step:
(A) By what factor does its volume increase?
We can use the ideal gas law to find the initial and final volumes of the balloon. Since the number of moles and temperature are constant, we can rearrange the equation to compare the initial and final volumes:
P₁V₁ = P₂V₂
Where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume, respectively.
Given:
P₁ = 115 kPa
P₂ = 55.0 kPa
Now, we need to solve for the volume ratio:
V₂/V₁ = P₁/P₂
Plugging in the values:
V₂/V₁ = 115 kPa / 55.0 kPa
Calculating this ratio will give us the factor by which the volume increases.
(B) How much work does the gas in the balloon do?
To calculate the work done by the gas, we can use the formula:
W = PΔV
Where W is the work done, P is the pressure, and ΔV is the change in volume. Here, we need to find the change in volume from initial to final conditions.
ΔV = V₂ - V₁
Using the obtained values for V₁ and V₂, we can calculate ΔV.
Finally, we can calculate the work done by multiplying the pressure difference (P₂ - P₁) with ΔV.
W = (P₂ - P₁) * ΔV
These steps should help us find the answers to both (A) and (B) based on the information provided.