Question

A cubic metal box with sides of 19 cm contains air at a pressure of 1 atm and a temperature of 253 K. The box is sealed so that the volume is constant, and it is heated to a temperature of 353 K. Find the force due to the internal air pressure on each wall of the box. _______kN

Answer 1

To solve this problem we will apply the concepts related to the Force based on pressure and temperature. Initially we will start from the definition of pressure that warns that it is the equivalent to the force applied to the unit of area, or any of those derived from this relationship. Subsequently, through the gas pressure-temperature ratio equations, we will set the desired pressure. The equation relating force and pressure is

`F = PA`

The value of final pressure is calculated as follows

`(P_1)/(P) = (T_1)/(T_2)`

`P = (T_2)/(T_1)P_1`

Therefore the value of force is

`F = ((T_2)/(T_1)P_1)A`

Replacing,

`F = ((353K)/(253K)(101325N/m^2))(19*10^(-2)m)^2`

`F = 5.1kN`

Therefore the force due to the internal air pressure on each wall of the box is 5.1kN