Question

A cubic box of volume 6.15 x 10-2 m3 is filled with air at atmospheric pressure at 15C. The box is closed and heated to 185C. what is the net force on each side of the box?

Answer 1

Answer on Question #46530, Physics, Mechanics | Kinematics | Dynamics

Question:

A cubic box of volume $6.15 \times 10^{-2} \, \text{m}^3$ is filled with air at atmospheric pressure at 15C. The box is closed and heated to 185C. What is the net force on each side of the box?

Answer:

Net force on each side of the box equals:

$$F = (P - P_a) A$$

where $P_a$ is atmospheric pressure, $P$ is pressure in the box, $A$ is area of the side.

The ideal gas law:

$$PV = nRT$$

where $P$ is the absolute pressure of the gas, $V$ is the volume of the gas, $n$ is the amount of substance of gas (measured in moles), $R$ is the ideal, or universal, gas constant, and $T$ is the absolute temperature of the gas.

For initial and final states:

$$P_a V = nRT_0$$ $$PV = nRT_1$$

Therefore:

$$P = P_a \frac{T_1}{T_0}$$

Area of the side equals:

$$A = a^2$$

where $a$ is length of the side. Assuming $V = a^3$:

$$A = V^{\frac{2}{3}}$$

Therefore:

$$F = P _ {a} \left(\frac {T _ {1}}{T _ {0}} - 1\right) V ^ {\frac {2}{3}} = 9320 \, N$$

Answer: 9320 N

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