Reycel05idn
Answered

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The volume (V) of gas varies directly as the temperature (t) and inversely as the pressure (p). If the volume is 40 cubic centimeters when the temperature is 5°K and the pressure is 4 pounds per square centimeter, what is the volume when the temperature is 9°K and the pressure 6 pounds per square centimeter.​

Sagot :

NataleighScottlynidn

Problem:

The volume (V) of gas varies directly as the temperature (t) and inversely as the pressure (p). If the volume is 40 cubic centimeters when the temperature is 5°K and the pressure is 4 pounds per square centimeter, what is the volume when the temperature is 9°K and the pressure 6 pounds per square centimeter.

Given:

  • Volume = 40
  • Temperature = 5 and 9
  • Pressure = 4 and 6

Solution:

To translate into variation statement a relationship involving combined variation between two quantities.

The statement, "The volume (V) of gas varies directly as the temperature (t) and inversely as the pressure (p)" translated into combined variation is v = kt/p where k is the constant of variation.

Solve if v is 40 when t is 5 and p is 4. So, find the constant using the equation of a combined variation.

  • v = kt/p
  • (40) = k(5)/(4)
  • 40 = 5k/4
  • 40 × 4 = 5k
  • 160 = 5k
  • 5k/5 = 160/5
  • k = 32

The constant of the variation is 32. In equation of variation.

  • v = 32t/p

Find v when t is 9 and p is 6. Substitute the equation using the constant of the variation that you obtained.

  • v = 32t/p
  • v = 32(9)/(6)
  • v = 288/6
  • v = 48

Answer:

∴ Therefore, the volume is 48 cubic cm to the combined variation.

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