Question

If an otherwise empty pressure cooker is filled with air of room temperature and then placed on a hot stove, what would be the magnitude of the net force F120F120F_120 on the lid when the air inside the cooker had been heated to 120∘C120∘C? Assume that the temperature of the air outside the pressure cooker is 20∘C20∘C (room temperature) and that the area of the pressure cooker lid is AAA. Take atmospheric pressure to be papap_a.

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The force on the lid when the air inside the cooker had been heated to 120°C is =
`0.34P_(a)A`

The force on the lid when the air inside the cooker had been heated to 20°C is =
`0.25P_(a)A`

The

Step-by-step explanation:

The main concept used to solve this problem is Pressure-Temperature Law.

Initially, find the pressure inside the pressure cooker by using the Pressure-Temperature Law. Then, find the force exerted by the air inside cooker on the lid of the cooker.

Fundamentals :

The Pressure-Temperature Law states that the pressure of the of a given gas held at constant volume is directly proportional to the Kelvin temperature. The increase in pressure results in an increase in the temperature and vice-versa.

The expression of the Pressure-Temperature Law is as follows:

`(P_(1))/(P_(2)) =(P_(2))/(T_(2))`

Here,
`P_(1)` and
`P_(2)`

are the initial and final pressures and
`T_(1)` and
`T_(2)`

are the initial and final temperatures respectively.

The force in terms of pressure can be given by the following expression.

F=(ΔP) A

Here, A is the area on which the pressure is applied and ΔP is the change in pressure

The step- step calculation is shown on the second,third,fourth, fifth image

Note:
`P_(a)` is the pressure of atmosphere