Question

A cylinder with a movable piston contains 20.5 moles of a monatomic ideal gas at a pressure of 2.86 × 105 Pa. The gas is initially at a temperature of 300 K. An electric heater adds 58600 J of energy into the gas while the piston moves in such a way that the pressure remains constant. It may help you to recall that CP = 20.79 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022 × 1023) times the number of moles of the gas. What is the temperature of the gas after the energy is added?

Answer 1

437.49 K

Step-by-step explanation:

Given:

The number of moles, n = 20.5 moles

Initial pressure P₁ = 2.86 × 10⁵ Pa

Initial temprature, T₁ = 300 K

Cp = 20.79 J/K/mole

Now

the Initial volume V₁ is given as

V₁ =
`(nRT)/(P)`

where, R is the gas constant

substituting the value in the above equation, we get

V₁ =
`(20.5* 8.314*300)/(2.86* 10^(5))`

or

V₁ =0.178 m³

the energy added (Q) =58600 J

also, we know that

Q = nCp(T ' - T )

where, T₂ is the final temperature

substituting the values in the equation, we get

58600 = 20.5 × 20.79 × (T ' - 300 )

T₂ - 300 = 137.49

or

T₂ = 437.49 K