Question

a tank having volume of 0.1m^3 contains helium gas at 150atm and fixed temperature at 27c calculate
1-how many ballons can the tank blow up if each field ballons is a shpere 0.3m in diameter at an absolute pressure of 1.2atm at the same temperature
2-the work done and which do the work
3-the change in internal energy
4-the quantity of heat and is this must added or removed

Answer 1

Answer on Question #43049-Physics-Molecular Physics-Thermodynamics

A tank having volume of $0.1\mathrm{m}^3$ contains helium gas at 150 atm and fixed temperature at 27°C calculate

1- how many balloons can the tank blow up if each field balloons is a sphere $0.3\mathrm{m}$ in diameter at an absolute pressure of 1.2 atm at the same temperature

Solution

At constant temperature $P_{1}V_{1} = P_{2}V_{2}$. (Boyle's law)

$$P_{1} = 150 \text{ atm} = 1.515 \cdot 10^{7} \text{ Pa}. \quad V_{1} = 0.1 \text{ m}^{3}.$$ $$P_{2} = 1.2 \text{ atm} = 1.212 \cdot 10^{5} \text{ Pa}.$$ $$V_{2} = \frac{P_{1}V_{1}}{P_{2}} = \frac{1.515 \cdot 10^{7} \cdot 0.1}{1.212 \cdot 10^{5}} = 12.5 \text{ m}^{3}.$$

Let $n$ is number of balloons and $V_{b}$ is the volume of each blown-up balloon.

$$V_{b} = \left(\frac{4\pi}{3}\right) r^{3} = \left(\frac{4\pi}{3}\right) \left(\frac{0.3}{2}\right)^{3} = 1.414 \cdot 10^{-2} \text{ m}^{3}.$$ $$n = \frac{V_{2}}{V_{b}} = \frac{12.5}{1.414 \cdot 10^{-2}} = 884.$$

The tank can blow up 884 balloons.

2- the work done and which do the work

Solution

In isothermal process gas expands to the new volume and work is done by the gas is

$$W = \int_{V_{1}}^{V_{2}} P dV,$$

where $P = \nu RT \cdot \frac{1}{V}$

$$W = \int_{V_{1}}^{V_{2}} \nu RT \cdot \frac{1}{V} dV = \nu RT \ln \frac{V_{2}}{V_{1}} = P_{1}V_{1} \ln \frac{V_{2}}{V_{1}} = 1.515 \cdot 10^{7} \cdot 0.1 \ln \frac{12.5}{0.1} = 7.31 \cdot 10^{6} \text{ J} = 7.31 \text{ MJ}.$$

$W$ have sign "+" , so the gas do the work.

3- the change in internal energy

Solution

Since the temperature and amount of gas is constant internal energy doesn't change:

$$\Delta U = 0.$$

4- the quantity of heat and is this must be added or removed

Solution

Since the internal energy doesn't change according to the First law of thermodynamics:

$$Q = W = 7.31 \, MJ.$$

As the gas expands, heat must be added.

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