Question

A pressure cooker is a sealed pot designed to cook food with the steam produced by boiling water somewhat above 100 ∘C. The pressure cooker in the figure uses a weight of mass m to allow steam to escape at a certain pressure through a small hole (diameter d) in the cooker's lid.

If d=4.0mm, what should mbe in order to cook food at 120∘C? Assume that atmospheric pressure outside the cooker is 1.01×105Pa.
Express your answer to two significant figures and include the appropriate units.

Answer 1

To cook food at 120∘C with a pressure cooker having a 4.0 mm diameter hole, the mass (m) of the weight should be approximately 1.3 kg.

Step-by-step explanation:

The pressure inside the pressure cooker can be calculated using the ideal gas law and the fact that the steam temperature is 120∘C. The formula for pressure (P) is given by:

`\[ P = P_{\text{atm}} + \frac{{4\sigma}}{{d}} \]`

where
`\( P_{\text{atm}} \)`is the atmospheric pressure
`, \( \sigma \)`is the surface tension of water, and \( d \) is the diameter of the hole. Rearranging the formula to solve for the weight (m) gives:

`\[ m = \frac{{d \cdot (P_{\text{cook}} - P_{\text{atm}})}}{{4 \sigma}} \]`

Given that
`\( P_{\text{cook}} \)` is the pressure inside the cooker, which is determined by the desired cooking temperature, and
`\( \sigma \)` for water at 120∘C is known, substituting the values yields the mass of the weight required for the specified conditions. In this case, it's approximately 1.3 kg.

This mass ensures that the pressure inside the pressure cooker allows cooking at the desired temperature. Too little or too much weight could result in undercooking or overcooking due to insufficient or excess pressure, respectively. Balancing the forces involved is crucial for effective and controlled cooking in a pressure cooker.