A balloon initially contains 40 m^3 of helium gas at atmospheric conditions of 100 kPa and 17°C. The balloon is connected by a valve to a large reservoir that supplies helium gas at 125 kPa and 30°C. Now the valve is opened, and helium can enter the balloon until pressure equilibrium with the helium at the supply line is reached. The material of the balloon is such that its volume increases linearly with pressure. If no heat transfer takes place during this process, determine 1) the final volume of the balloon. 2) the boundary work done during this process 3) the final temperature in the balloon.

Respuesta :

The final volume is 56. 47 m^3

Work done is -2,058. 75 Joules

The final temperature in the balloon is 30° C

How to determine the final volume

Using the formula:

P1V1/T1 = P2V2/T2

Where P1 and P2 = initial and final pressures

V1 and V2 = initial and final volumes

T1 and T2 = initial and final temperature

From the formula, make 'V2' the subject

V2 =P1V1T2/ P2T1

V2 = 100 × 40 × 30 / 125 × 17

V2 = 120000 / 2125

V2 = 56. 47 m^3

The final volume is 56. 47 m^3

How to determine the work done

Using the formula

Work done = - External pressure × change in volume

External pressure is from the valve = 125Kpa

Change in volume = V2 - V1 = 56. 47 - 40 = 16. 47 m^3

Work done = - 125 × 16. 47 = -2,058. 75 Joules

3. The final temperature in the balloon is 30° C

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