Question

A balloon contains 46.3 L of Helium at 42 oC, and 2.01 atm is released into the air. At a certain altitude, the temperature falls to 21 oC, and the pressure falls to 0.25 atm. What is the volume of the balloon under these conditions?

A. 3.5 L
B. 35.0 L
C. 347.5 L
D. 3475.0 L
E. None of the Above

Answer 1

A balloon contains 46.3 L of Helium at 42 oC, and 2.01 atm is released into the air. At a certain altitude, the temperature falls to 21 oC, and the pressure falls to 0.25 atm. What is the volume of the balloon under these conditions?

A. 3.5 L

B. 35.0 L

C. 347.5 L

D. 3475.0 L

E. None of the Above

Solution:

Consider 2 state of the thermodynamic system:

1). $V_{1} = 46.3L;$

$$T _ {1} = 4 2 \circ C = 3 1 5. 1 5 K;$$ $$P _ {1} = 2. 0 1 a t m.$$

2). $V_{2}$ is unknown;

$$T _ {2} = 2 1 \circ C = 2 9 4. 1 5 K;$$ $$P _ {2} = 0. 2 5 a t m.$$

According to Ideal gas law:

$$V _ {2} = \frac {n R T _ {2}}{P _ {2}} = \frac {P _ {1} V _ {1} R T _ {2}}{R T _ {1} P _ {2}} = \frac {P _ {1} V _ {1} T _ {2}}{T _ {1} P _ {2}} = \frac {2 . 0 1 a t m \times 4 6 . 3 L \times 2 9 4 . 1 5 K}{3 1 5 . 1 5 K \times 0 . 2 5 a t m} = 3 4 7. 5 L$$

Answer: C. 347.5 L.