# StudySquare

This page covers the following topics:

1. Pressure and force

2. Pressure in gases

Pressure is defined as the effect of a force on a given area. It can be calculated by dividing the force over the area it is acting on. Pressure is measured in pascals, Pa.

Pressure is inversely proportional to the area a force is exerted on. This means that a force exerted on a lower area causes a higher pressure.

The ideal gas equation relates pressure, volume, temperature and amount of gas. It is important to use the SI units of all the variables in the equation, the gas constant is 8.31 J K⁻¹ mol⁻¹, one mole is Avogadro constant = 6.02 × 10²³, the temperature needs to be given in kelvin (K). The absolute temperature in K can be found by adding 273.15 to the temperature in °C.

There are three specific cases for the ideal gas equation. When only pressure and volume are changing, it is called Boyle’s law and yields p₁V₁ = p₂V₂. When only pressure and temperature are changing, it is called Gay-Lussac’s law and yields p₁/T₁ = p₂/T₂. When only volume and temperature are changing, it is called Charles’ law and yields V₁/T₁ = V₂/T₂.

# 1

Anna's hand has a surface area of 0.06 m². She pushes a circular button of surface area 0.0018 m² with a force of 7 N. Calculate the pressure Anna exerts on the button.

The force exerted by Anna is acting over the area of the button rather than her hand; thus, 0.0018 m² should be used in calculations.

p = F ÷ A

p = 7 N ÷ 0.0018 m² = 3890 Pa (3 s. f.)

3890 Pa

# 2

Explain why a sharper knife is better at cutting than a blunt knife.

The force being exerted on what is being cut is spread over a smaller surface area when using a sharp knife. Since pressure is inversely proportional to the area a force is exerted on and the area is smaller for a sharper knife, the sharper knife exerts a greater pressure on what is being cut, which makes it better at cutting things than a blunt knife.

A sharper knife has a lower area which results in a higher exerted pressure.

# 3

A wooden block with a base area of 0.08 m² and a weight of 70 N is placed on the same ground as an aluminium block with a base area of 0.23 m² and a weight of 200 N. Find which block exerts a greater pressure on the ground below them.

p = F ÷ A

for the wooden block: pressure = 70 N ÷ 0.08 m² = 875 Pa

for the aluminium block: pressure = 200 N ÷ 0.23 m² = 870 Pa (3 s. f.)

Therefore, the wooden block exerts a greater pressure on the ground.

wooden

# 4

16 moles of hydrogen occupy a volume of 5.2 dm³ at a pressure of 112 kPa. Using the ideal gas equation, calculate the temperature in kelvins.

5.2 dm³ = 0.0052 m³

112 kPa = 112000 Pa

pV = nRT

T = pV/nR

T = (112000 × 0.0052)/(16 × 8.31) = 4.38 K (3 s. f.)

4.38 K

# 5

A box of weight 20 N and base area 0.09 m² sits on a table. Calculate the pressure exerted by the vase on the table.

p = F ÷ A

pressure = 20 N ÷ 0.09 m² = 222 Pa (3 s. f.)

222 Pa

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