Which one of the following is not the unit of pressure?

Correct — C, J/m². Pressure is force spread over an area, so any unit of pressure must reduce to a force unit divided by an area unit. N/m² is precisely that, and the pascal is defined as one newton per square metre, so the first two options are the same unit under two names; the bar is a larger practical unit of the same quantity, worth a hundred thousand pascals. J/m² is energy over area, not force over area. Work out what it reduces to and you get N·m ÷ m², that is N/m — force per unit length, which is the unit of surface tension and of surface energy. Energy per unit volume, J/m³, would have had the dimensions of pressure; energy per unit area does not.

• (a)pascal (Pa) — The SI unit of pressure itself, named after Blaise Pascal and defined as one newton per square metre.
• (b)N/m² — This is the definition of pressure written out — force divided by area. It is the pascal spelt in base units, not a different quantity.
• (d)bar — A practical unit of pressure equal to a hundred thousand pascals, which is a little less than standard atmospheric pressure. Weather and engineering use it constantly.

Pressure is defined as force per unit area, so its dimensions are those of force divided by area. The SI unit is the pascal, one newton per square metre, and larger practical units such as the bar and the atmosphere are simply multiples of it. Checking a candidate unit means reducing it to base units and comparing.

Three of the options announce themselves as pressure units and the fourth has to be tested. The test is quick: a joule is a newton-metre, so J/m² is N·m ÷ m², which cancels to N/m. Force per unit length is what holds the surface of a liquid together, which is why that unit belongs to surface tension; it is also read as energy per unit area of surface, and the two readings agree because stretching a surface by unit area costs exactly that much work. The near-miss worth remembering is one power of length away. J/m³ — energy per unit volume — does reduce to N/m², so energy density and pressure share a unit, which is the reason the energy stored in a compressed gas can be written as pressure times volume. Note also that the pascal is a small unit: atmospheric pressure at sea level is about 101325 pascals, so everyday pressures are usually quoted in kilopascals or bars.

• Pressure is force per unit area, and one pascal is one newton per square metre.
• One bar equals 100000 pascals; standard atmospheric pressure is 101325 pascals, a little over one bar.
• J/m² reduces to N/m, force per unit length — the unit of surface tension and of surface energy.
• J/m³, energy per unit volume, does have the dimensions of pressure, which is why energy density and pressure share a unit.
• Older pressure units still in use include the torr and the millimetre of mercury, with 760 millimetres of mercury equal to one atmosphere.

• Assuming that any unit containing a square metre in the denominator must be a pressure.
• Confusing J/m² with J/m³, only the second of which reduces to a pressure.
• Treating the pascal and N/m² as different quantities because they are written differently.

Asked as a negative unit-identification item, answerable by reducing each option to base units rather than by recall.

• practice — not a real PYQ

  The unit of surface tension is

  • (a)N/m²
  • (b)N/m
  • (c)N·m
  • (d)N·s

  Answer(b) N/m — force per unit length, which is the same as the energy per unit area of surface, J/m².

• practice — not a real PYQ

  One bar is equal to

  • (a)10³ pascal
  • (b)10⁴ pascal
  • (c)10⁵ pascal
  • (d)10⁶ pascal

  Answer(c) 10⁵ pascal — slightly less than standard atmospheric pressure, which is 101325 pascal.