Question

A person cooks a meal in a 30-cm-diameter pot that is covered with a well-fitting lid and lets the food cool to the room temperature of 20°C. The total mass of the food and the pot is 8 kg. Now the person tries to open the pan by lifting the lid up. Assuming no air has leaked into the pan during cooling, determine if the lid will open or the pan will move up together with the lid.

Answer 1

Answer:Pan will move up together with the lid.

Explanation:

Given

diameter of pot(d)=30 cm

Temperature of room$=20^{\circ}\approx 293 K$

assume vapor pressure of water at 293 K is $P_v=2.3 kPa, P_{atm}=101.32 kPa$

mass of food and the pot=8 kg

Pressure Difference $\Delta P=P_{atm}-P_{v}=101.3-2.3=99 kPa$

Area of lid $A=\frac{\pi d^2}{4}=0.0706 m^2$

Force due to Pressure difference $=\Delta P\times A$

$=99\times 10^3\times 0.0706=6998.805 N$

Downward Force opposing it will be weight=mg

$W=8\times 9.8=78.4 N$

Downward force is less than force due to pressure difference thus Pan will move up together with the lid