i cant figure this one out! :(
a balloonist is preparing a trip in a helium balloon. the trip begins in early morning at a temp of 15 degrees Celcius. By mid afternoon, the temp has increased to 30 degrees C. assuming the pressure remains constant at 1.00 atm, for each mole of helium, calculate:
1. the initial and final volume
2. the change in internal energy
3. the work done by helium
4. change in enthalpy
To answer these questions, we need to use the ideal gas law equation, which is PV = nRT, where P represents pressure, V represents volume, n represents the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Let's start with solving the problems:
1. The initial and final volume:
To find the initial volume, we need to convert the temperature from Celsius to Kelvin. Adding 273 to the Celsius value will give us the temperature in Kelvin.
Initial temperature (in Kelvin) = 15°C + 273 = 288 K
Using the ideal gas law equation, we can find the initial volume:
P(initial) * V(initial) = n * R * T(initial)
Since we know that the pressure remains constant (1.00 atm) and the number of moles is not given, we can assume it to be 1 mole.
1 atm * V(initial) = 1 mole * R * (288 K)
V(initial) = R * (288 K)
Similarly, we can find the final volume using the final temperature (30°C + 273 = 303 K) and the same assumption of 1 mole:
1 atm * V(final) = 1 mole * R * (303 K)
V(final) = R * (303 K)
2. The change in internal energy:
The change in internal energy (ΔU) can be found using the equation ΔU = U(final) - U(initial). Since we have no information about the system's specifics, such as any chemical reactions or changes in the number of particles, we can assume that ΔU is zero.
3. The work done by helium:
The work done by a gas can be calculated using the equation W = -PΔV, where P is the pressure, and ΔV is the change in volume. As we know, the pressure remains constant at 1.00 atm. Therefore, the work done can be calculated as:
W = -1.00 atm * (V(final) - V(initial))
4. The change in enthalpy:
The change in enthalpy (ΔH) can be found using the equation ΔH = Q + W, where Q is the heat transfer to the system, and W is the work done by the system. Since no information about heat transfer is given, we can assume that ΔH is equal to the work done:
ΔH = W
Please note that the numerical values of the specific heat capacity and the gas constant were not provided, so we cannot calculate the exact numerical values for V, W, or ΔH.