Question

Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. the initial temperature of the gas is 27.0c and the pressure is constant. as part of a machine design project, calculate the final temperature of the gas after it has done 2.40 * 103 j of work.

Answer 1

We have to know final temperature of the gas after it has done 2.40 X 10³ Joule of work.

The final temperature is: 75.11 °C.

The work done at constant pressure, W=nR(T₂-T₁)

n= number of moles of gases=6 (Given), R=Molar gas constant, T₂= Final temperature in Kelvin, T₁= Initial temperature in Kelvin =27°C or 300 K (Given).

W=2.4 × 10³ Joule (Given)

From the expression,

(T₂-T₁)=$\frac{W}{nR}$

(T₂-T₁)= $\frac{2.40 X 10^{3} }{6 X 8.314}$

(T₂-T₁)= 48.11

T₂=300+48.11=348.11 K= 75.11 °C

Final temperature is 75.11 °C.

Answer 2

The final temperature of the gas after it has done the given work is determined as 75.11 ⁰C.

Final temperature of the gas

The final temperature of the gas can be determined from ideal gas equation as shown below;

PV = nRT

W = nRΔT

ΔT = W/nR

ΔT = (2400)/(6 x 8.314)

ΔT = 48.11 ⁰C

T₂ = ΔT + T₁

T₂ = 48.11 + 27

T₂ = 75.11 ⁰C

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