Question

В баллоне вместимостью V = 10 л находился гелий под давлением p1 = 10 атм при температуре t1 = 27 С. после того как из баллона был выпущен газ массой m = 10 г, температура в баллоне была понижена до t2 = 17 C. Определите давление гелия, оставшегося в баллоне.

Answer 1

Calculation of the remaining pressure of helium in the balloon

To determine the remaining pressure of helium in the balloon after releasing a certain amount of gas, we can use the ideal gas law equation:

PV = nRT

Where: - P is the pressure of the gas - V is the volume of the gas - n is the number of moles of the gas - R is the ideal gas constant - T is the temperature of the gas

In this case, we are given the initial conditions of the balloon: - Volume (V) = 10 L - Pressure (P1) = 10 atm - Temperature (T1) = 27°C

We are also given that a certain amount of gas with a mass (m) of 10 g was released from the balloon, and the temperature inside the balloon decreased to T2 = 17°C.

To solve for the remaining pressure (P2) of the helium in the balloon, we need to calculate the number of moles of helium before and after the gas is released.

Calculation of the number of moles of helium before and after gas release

To calculate the number of moles of helium, we can use the ideal gas law equation rearranged to solve for n:

n = PV / RT

Before the gas is released, the number of moles of helium (n1) can be calculated using the initial conditions:

n1 = (P1 * V) / (R * T1)

After the gas is released, the number of moles of helium (n2) can be calculated using the final conditions:

n2 = (P2 * V) / (R * T2)

Calculation of the remaining pressure of helium

Since the number of moles of helium remains constant, we can equate n1 and n2:

(P1 * V) / (R * T1) = (P2 * V) / (R * T2)

Simplifying the equation:

P2 = (P1 * T2 * V) / (T1 * V)

Simplifying further:

P2 = (P1 * T2) / T1

Now we can substitute the given values into the equation to calculate the remaining pressure of helium in the balloon.

Given: - P1 = 10 atm - T1 = 27°C = 300 K - T2 = 17°C = 290 K

Substituting the values:

P2 = (10 atm * 290 K) / 300 K

Calculating the value:

P2 = 9.6667 atm

Therefore, the remaining pressure of helium in the balloon is approximately 9.6667 atm.

Please note that the calculations assume ideal gas behavior and neglect any other factors that may affect the pressure, such as the compressibility of the gas or the expansion of the balloon.